Question

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

Answer 1

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)

⇒ $f^{-1}(x)=\frac{19-14}{5}=1$

Answer 2

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!