Question

Given the function f(x)= 5(x+4) -6 solve for the inverse function when x = 9

Answer 1

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

Explanation:

If f(x) = 5(x+4)-6

Then we have to find the inverse of this first.

Let the function is in the form of y = 5(x+4) - 6

then 5(x+4) = y + 6

x + 4 = (y + 6)/5

x = (y + 6)/5 - 4

Now converting this equation to the inverse of the function

`f^(-1)` = (x+6)/5 - 4

Now
`f^(-1)(9)` = (9 + 6)/5 - 4

= 15/5 - 4 = 3 - 4 = (-1)

Answer 2

Answer:
`y^(-1)=-1`

Explanation:

Rewrite the function as following:

`y=5(x+4)-6`

Now, you must solve for x as you can see below:

`y=5x+20-6\\y=5x+14\\y-14=5x\\x=(y-14)/(5)`

Rewrite it as following:

`y=(x-14)/(5)`

Now substitute x=9 into the function above, then, you obtain:

`y=(9-14)/(5)`

`y^(-1)=-1`