0. Functions

Suppose that the range of g lies in the domain of f so that the composition fog is defined. If f and g are one-to-one, can anything be said about fog? Give reasons for your answer.

Each of Exercises 19–24 gives a formula for a function y=f(x) and shows the graphs of f and f^(-1). Find a formula for f^(-1) in each case.

f(x)=x²+1, x≥0

Each of Exercises 19–24 gives a formula for a function y=f(x) and shows the graphs of f and f^(-1). Find a formula for f^(-1) in each case.

f(x)=x³-1

Each of Exercises 19–24 gives a formula for a function y=f(x) and shows the graphs of f and f^(-1). Find a formula for f^(-1) in each case.

f(x)=(x+1)², x≥-1

Find the inverse of the function f(x)=mx, where m is a constant different from zero.

Show that the graph of the inverse of f(x)=mx+b, where m and b are constants and m≠0, is a line with slope 1/m and y-intercept -b/m.

Find the inverse of f(x)=x+b (b constant). How is the graph of f^(-1) related to the graph of f?

Find the inverse of f(x)=-x+1. Graph the line y=-x+1 together with the line y=x. At what angle do the lines intersect?

In Exercises 41–44:

a. Find f⁻¹(x).

41. f(x) = 2x + 3, a = −1

In Exercises 41–44:

a. Find f⁻¹(x).

42. f(x) = (x + 2) / (1 − x), a = 1/2

In Exercises 41–44:

a. Find f⁻¹(x).

43. f(x) = 5 − 4x, a = 1/2

In Exercises 41–44:

a. Find f⁻¹(x).

44. f(x) = 2x², x ≥ 0, a = 5