Verified Answer :

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:

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

Step-by-step 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

    \(x+6=5(y+4)\)

 ⇒         \(x+6=5y+20\)

 ⇒         \(x+6-20=5y\)

 ⇒         \(y=\frac{x-14}{5}\)

Step4: Replace y by \(f^{-1}(x)\)

gives     \(f^{-1}(x)=\frac{x-14}{5}\)

When x=19      (given)

⇒ \(f^{-1}(x)=\frac{19-14}{5}=1\)