Answer:
[tex]\frac{11}{2}[/tex]
Step-by-step explanation:
To obtain the inverse of f(x)
let y = f(x) and rearrange making x the subject, that is
y = 2x - 1 ( add 1 to both sides )
y + 1 = 2x ( divide both sides by 2 )
[tex]\frac{y+1}{2}[/tex] = x
Change y back into terms of x with x = [tex]f^{-1}[/tex](x) , thus
[tex]f^{-1}[/tex](x) = [tex]\frac{x+1}{2}[/tex]
Evaluate g(3) and substitute the value obtained into [tex]f^{-1}[/tex](x)
g(3) = 3² + 1 = 9 + 1 = 10, then
[tex]f^{-1}[/tex] (10) = [tex]\frac{10+1}{2}[/tex] = [tex]\frac{11}{2}[/tex]
