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