HELP ASAP PLEASE ! algerbra 2, finding inverses functions and relations help

Question

4) Given f(x)=2x−3 and its inverse f−1(x)=x+32, find the following functions: 

 

a) [f∘f−1](x)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

b) [f−1∘f](x)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5) Given f(2)=5, f(5)=7, and f(7)=12, what is the value of f−1(f−1(12))? 

 

Answer 1

f(x) = 2x -3, f^-1(x) = (x+3)/2

the composition of f(f^-1(x)) or f^-1(f(x)) = x

that's how inverses work, they bring you back to where you started. You start with x, then do a function, then an inverse function, you get right back to x

f(f^-1(12)) = 12. Start with 12, and end with 12, regardless of the specific f(x)

BUT you have f^-1(f^-1(x)) which does depend on the specific function

f(5)=7, f^-1(7) = 5

f(7) = 12, f^-1= 7

f^-1(f^-1(12)) = f^-1(7) = 5

f(f(5)) took you from 5 to 12

f^-1(f^-1(12) takes you back from 12 to 5