Question

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

Answer 1

Answer: $y^{-1}=-1$

Step-by-step explanation:

Rewrite the function as following:

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

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

$y=5x+20-6\\y=5x+14\\y-14=5x\\x=\frac{y-14}{5}$

Rewrite it as following:

$y=\frac{x-14}{5}$

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

$y=\frac{9-14}{5}$

$y^{-1}=-1$

Answer 2

Answer:

$f^{-1}(9) = -1$

Step-by-step 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)