Question

Given the function f(x) = 5(x+4) − 6, solve for the inverse function when x = 19.

Answer 1

Y = 5(x+4)-6
x = 5(y+4)-6
x = 5y +20 - 6
x= 5y +14
5y = x-14
y = (x-14)/5

when x = 19, y = (19-14)/5
y = 5/5
y=1

In short, Your Answer would be Option 2

Hope this helps!

Answer 2

The answer is 1 i.e the inverse function will be 1 when x=19

Explanation:

Given
`f(x)=5(x+4)-6`

we have to solve for inverse function

Step 1: Replace f(x) with y.

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

Step 2: Now replace all x with y and all y with x, we get

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

Step 3: Solve for y

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

⇒
`x+6=5y+20`

⇒
`x+6-20=5y`

⇒
`y=(x-14)/(5)`

Step4: Replace y by
`f^(-1)(x)`

gives
`f^(-1)(x)=(x-14)/(5)`

When x=19 (given)

⇒
`f^(-1)(x)=(19-14)/(5)=1`