How do I solve and graph this problem?

Question

Consider the function f(x) = −3x+ 5. Compute the inverse function, f^-1(x), to f(x) and verify that
(f ◦ f^-1)(x) =(f^-1 ◦ f)(x) = x. Furthermore, sketch both f(x) and its inverse on the same graph

Answer 1

Hi Terry,

 

to find the inverse of f(x), we assume y=f(x). So, y=-3x + 5.

 

now interchanging the variables. We can write,

x=-3y+5

=> 3y= 5-x

=> y=5/3 - x/3

therefore, inverse of f(x)= 5/3 -x/3

 

now we r going to find the LHS and you would do the RHS, okay?

 

LHS=f(inverse of f(x))

      =f(5/3 -x/3)

      =- 3(5/3 -x/3) + 5

      =x

do the RHS by yourself.

I cannot draw the graph here. Good luck