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)
⇒ \(f^{-1}(x)=\frac{19-14}{5}=1\)
