Question

Write the inverse function for the function, ƒ(x) =1/2x + 4. Then, find the value of ƒ^ -1(4). Type your answers in the box.

ƒ^ -1(x) =

ƒ ^-1(4) =

Answer 1

Answers:

The inverse function is ƒ ^-1 (x)= 2x-8

The value of ƒ ^-1 (4)= 0

Hope this helps <3

Answer 2

f⁻¹(x) = 2x - 8

f⁻¹(4) = 2 × 4 - 8

f⁻¹(4) = 0

Explanation:

`f(x) = (1)/(2) x + 4\\x = (1)/(2) f^(-1)(x) + 4\\x - 4 = (1)/(2) f^(-1)(x)\\2x - 8 = f^(-1)(x)\\f^(-1)(x) = 2x - 8`

Let's test it

`f^(-1)(f(x)) = 2(f(x)) - 8\\f^(-1)(f(x)) = 2( (1)/(2)x + 4) - 8\\f^(-1)(f(x)) = (2)/(2)x + 8 - 8\\f^(-1)(f(x)) = x`

So we do indeed have the inverse function, so using that we can plug in the values requested:

f⁻¹(x) = 2x - 8

f⁻¹(4) = 2 × 4 - 8

f⁻¹(4) = 0