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

Answer:

$f^{-1}(8)=1.5$

Step-by-step explanation:

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

$y=2x+5\\ \\2x=y-5\\ \\x=\dfrac{y-5}{2}$

Now, change y into x and x into y:

$y=\dfrac{x-5}{2}\\ \\f^{-1}(x)=\dfrac{x-5}{2}$

Substitute x=8 into $f^{-1}(x)$ expression:

$f^{-1}(8)=\dfrac{8-5}{2}\\ \\f^{-1}(8)=\dfrac{3}{2}=1.5$

Answer 2

Answer:

3/2

Step-by-step 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