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.

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.

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?

What can you conclude about the inverses of functions whose graphs are lines perpendicular to the line y=x?

In Exercises 41–44:

a. Find f⁻¹(x).

41. f(x) = 2x + 3, a = −1