Determine the domains of the following functions. f (x) = 1 / x(x + 3)
> Compute the numbers. (.01)-1.5
> Compute the numbers. (1/8)-2/3
> In Exercises 7–12, express f (x) + g(x) as a rational function. Carry out all multiplications. f (x) = 2 / x - 3, g(x) = 1 / x + 2
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) - g(x)
> Compute the numbers. 4-1/2
> Compute the numbers. (81)0.75
> Compute the numbers. 160.5
> Let f (x) = x / x - 2, g(x) = 5 – x / 5 + x, and h(x) = x + 1 / 3x - 1. Express the following as rational functions. f (x) - g(x)
> Describe the domain of the function. g(x) = 1 / √(3 – x)
> Compute the numbers. 91.5
> Refer to the function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16. What is the additional cost of increasing the radius from 3 inches to 6 inches? g (x)
> Compute the numbers. (1.8)0
> Compute the numbers. (27)2/3
> Find the points of intersection of the pairs of curves in Exercises 31–38. y = 30x3 - 3 x2, y = 16x3 + 25x2
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. g(x)h(x)
> Compute the numbers. (25)3/2
> Compute the numbers. 163/4
> Compute the numbers. 84/3
> Graph the following equations. y = -2x + 3
> Compute the numbers. (-5)-1
> Let f (x) = 3√x and g(x) = 1 / x2. Calculate the following functions. Take x > 0. g (f (x))
> Compute the numbers: (.01)-1
> Refer to the function f (r), which gives the cost (in cents) of constructing a 100-cubic-inch cylinder of radius r inches. The graph of f (r) is shown in Fig. 16. Interpret the fact that the point (3, 162) is the lowest point on the graph of the functio
> Use the laws of exponents to simplify the algebraic expressions. Your answer should not involve parentheses or negative exponents. √x (1/4x)5/2
> Compute the numbers. (½)-1
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x)/h(x)
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x) + g(x)
> Find an equation of the given line. Horizontal through (√7, 2)
> Find an equation of the given line. Slope is -2; x-intercept is -2
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> Find an equation of the given line. Slope is 2; x-intercept is -3
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. f (h(x))
> Evaluate each of the functions in Exercises 37–42 at the given value of x. f (x) = |x|, x = -2/3
> Find an equation of the given line. x-intercept is -π; y-intercept is 1
> Find an equation of the given line. x-intercept is 1; y-intercept is -3
> Find an equation of the given line. Horizontal through (2, 9)
> Find an equation of the given line. (- 1/2, - 1/7) and (2/3, 1) on line
> Find an equation of the given line. (0, 0) and (1, 0) on line
> Find an equation of the given line. (1/2, 1) and (1, 4) on line
> Find an equation of the given line. (5/7, 5) and (- 5/7 , -4) on line
> Find an equation of the given line. Slope is 7/3; (1/4, - 2/5) on line
> Find an equation of the given line. Slope is 1/2 ; (2, 1) on line
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. g (h(t))
> Find an equation of the given line. Slope is 2; (1, -2) on line
> Find an equation of the given line. Slope is -1; (7, 1) on line
> Find the slopes and y-intercepts of the following lines. 4x + 9y = -1
> Find the slopes and y-intercepts of the following lines. y = x/7 - 5
> Find the slopes and y-intercepts of the following lines. y = 6
> Let f (x) = [1/(x + 1)] - x2. Evaluate f (a + 1).
> Let f (x) = x2 - 2. Evaluate f (a - 2).
> Let f (x) = 2x + 3x2. Evaluate f (0), f (- 1/4), and f (1/√2).
> Let f (x) = x3 +1 /x. Evaluate f (1), f (3), f (-1), f (- 12), and f (√2).
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. g (f (x))
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> Suppose that $7000 is deposited in a savings account that pays a rate of interest r per annum, compounded annually, for 20 years. (a) Express the account balance A(r) as a function of r. (b) Calculate the account balance for r = .07 and r = .12.
> Suppose that $15,000 is deposited in a savings account that pays a rate of interest r per annum, compounded annually, for 10 years. (a) Express the account balance A(r) as a function of r. (b) Calculate the account balance for r = 0.04 and r = 0.06
> Suppose that $7000 is deposited in a savings account that pays 9% per annum, compounded biannually, for t years. (a) Express the account balance A(t) as a function of t, the number of years that the principal has been in the account. (b) Calculate the ac
> Suppose that $15,000 is deposited in a savings account that pays 4% per annum, compounded monthly, for t years. (a) Express the account balance A(t) as a function of t, the number of years that the principal has been in the account. (b) Calculate the acc
> Use the laws of exponents to simplify the algebraic expressions. 3√x (8x2/3)
> Use the laws of exponents to simplify the algebraic expressions. x3/2/ √x
> Use the laws of exponents to simplify the algebraic expressions. xy3 / x-5y6
> Use the laws of exponents to simplify the algebraic expressions. (√(x + 1))4
> The revenue R(x) (in thousands of dollars) that a company receives from the sale of x thousand units is given by R(x) = 5x - x2. The sales level x is in turn a function f (d) of the number d of dollars spent on advertising, where Express the revenue as
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. h(g(x))
> The population of a city is estimated to be 750 + 25t + .1t2 thousand people t years from the present. Ecologists estimate that the average level of carbon monoxide in the air above the city will be 1 + .4x ppm (parts per million) when the population is
> Exercises 43–46 relate to Fig. 13. When a drug is injected into a person’s muscle tissue, the concentration y of the drug in the blood is a function of the time elapsed since the injection. The graph of a typical time&
> Simplify (100)3/2 and (.001)1/3.
> Simplify (81)3/4, 85/3, and (.25)-1.
> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. h(f (x))
> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. f (h(x))
> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. h(g(x))
> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. g(h(x))
> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. g(f (x))
> Let f (x) = x2 - 2x + 4, g(x) = 1/x2, and h(x) = 1/(√x - 1). Determine the following functions. f (g(x))
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. h (f (t))
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) + g(x)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. g(x) - h(x - 3)
> Relate to the function whose graph is sketched in Fig. 12. For what values of x is f (x) ≤ 0? (2, 3) y = f(x) + 1 + 5 (7, –1)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) + h(x)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. g(x) - h(x)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) - g(x + 1)
> Let f (x) = x/(x2 - 1), g(x) = (1 - x)/(1 + x), and h(x) = 2/(3x + 1). Express the following as rational functions. f (x) - g(x)
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. g(x)h(x)
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x)/h(x)
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x)g(x)
> If f (x) = x2 - 3x, find f (0), f (5), f (3), and f (-7).
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x)h(x)
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x) - g(x)
> Let f (x) = x2 - 2x, g(x) = 3x - 1, and h(x) = √x. Find the following functions. f (x) + g(x)
> Relate to the function whose graph is sketched in Fig. 12. For what values of x is f (x) ≤ 0? (2, 3) y = f(x) + 1 + 5 (7, –1)
> Find the points of intersection of the curves y = -x2 + x + 1 and y = x - 5.
> Find the points of intersection of the curves y = 5x2 - 3x – 2 and y = 2x - 1.
> Find the zeros of the quadratic function y = -2x2 - x + 2.
> Find the zeros of the quadratic function y = 5x2 - 3x - 2.
> Factor the polynomials. x5 - x4 - 2x3
> Factor the polynomials. 18 + 3x - x2
> Let f (x) = x6, g(x) = x / 1 - x, and h(x) = x3 - 5x2 + 1. Calculate the following functions. f (g(x))
> Factor the polynomials. 3x2 - 3x - 60
> Factor the polynomials. 5x3 + 15x2 - 20x
