Answer:
\(\text{The value of }f^{-1}(8)\text{ is }\frac{3}{2}\)
Step-by-step explanation:
Given the function
\(f(x)=2x+5\)
\(\text{we have to find the value of }f^{-1}(8)\)
First we have to find the inverse
Step 1: Put f(x)=y, the equation becomes
\(y=2x+5\)
Step 2: Replace x to y and y to x, we get
\(x=2y+5\)
Step 3: Solve for y and then replace it with \(f^{-1}x\)
\(x-5=2y\)
\(y=\frac{x-5}{2}\)
\(f^{-1}(x)=\frac{x-5}{2}\)
Now substitute x=8, we get
\(f^{-1}(8)=\frac{8-5}{2}=\frac{3}{2}\)
\(\text{hence, the value of }f^{-1}(8)\text{ is }\frac{3}{2}\)
