Question

Two functions f and g are defined on the set R of real numbers by f(x) = 2x - 1 and g(x) =x² + 1. Find the value of tps://tex.z-dn.net/?f=f%5E%7B-1%7D" id="TexFormula1" title="f^{-1}" alt="f^{-1}" align="absmiddle" class="latex-formula">og (3)

Answer 1

Answer:

$\frac{11}{2}$

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 )

$\frac{y+1}{2}$ = x

Change y back into terms of x with x = $f^{-1}$(x) , thus

$f^{-1}$(x) = $\frac{x+1}{2}$

Evaluate g(3) and substitute the value obtained into $f^{-1}$(x)

g(3) = 3² + 1 = 9 + 1 = 10, then

$f^{-1}$ (10) = $\frac{10+1}{2}$ = $\frac{11}{2}$