determine, find, and graph...............

Question

Given f(x)=5x+8. (a) Determine whether f(x) is one-to-one. (b) Find a formula for its inverse. (c) Graph f(x) and f^(-1) (x) on the same axis

Answer 1

a) Since f(x) = 5x+8 is increasing everywhere, f(x) is ono-to-one.

 

b) Switch x and y, and solve for y,

x = 5y+8

=> y = f^-1(x) = (x-8)/5

 

c) Graph both f(x) and f^-1(x), and pay attention that f^-1(x) can be obtained by reflecting f(x) over y = x.