Question

If f(x) and f^-1(x) are inverse functions of each other adn f(x) - 2x+5, what is f^-1(8)?

Answer 1

3/2

Explanation:

f(x) = 2x+5

f⁻¹(2x+5) = x

2x+5 = 8 => 2x+5 = 8 => 2x = 3 =>

=> x = 3/2

=> f⁻¹(8) = 3/2

Answer 2

`f^(-1)(8)=1.5`

Explanation:

If y=f(x)=2x+5, to find the inverse function express x n terms of y:

`y=2x+5\\ \\2x=y-5\\ \\x=(y-5)/(2)`

Now, change y into x and x into y:

`y=(x-5)/(2)\\ \\f^(-1)(x)=(x-5)/(2)`

Substitute x=8 into
`f^(-1)(x)` expression:

`f^(-1)(8)=(8-5)/(2)\\ \\f^(-1)(8)=(3)/(2)=1.5`