Question

Suppose that f(x)=4x+5. What is f^-1 (f^-1(9)) ?

Answer 1

Explanation:

the inverse of the inverse of a function is the function itself

It's like going and coming back

• f^-1(f^(-1)9) = f(9)
• f(9) = 4*9+5
• f(9) = 36+5
• f(9) = 41

Answer 2

9

Explanation:

The inverse of the inverse is the input

f^-1 (f^-1(9)) = 9

As a proof

f(x) = 4x+5

y = 4x+5

Exchange x and y

x = 4y+5

Solve for y

(x+5) = 4y

(x+5)/4 = y

f^-1 (x) = ( x-5)/4

Then find the inverse of this function

y = ( x-5) /4

Exchange x and y

x = (y-5)/4

4x = y-5

4x+5 = y

Which gives us the original function back

f^-1( input) = 4x+5

Using the value given

f^-1 (9) = ( 9-5)/4=4/4 =1

Using the 1 from the previous part as the input

f^-1( 1) = 4*1+5 = 4+5 = 9