Question

Given f(x) = X-1/2
solve for f1(5).

Answer 1

as you already know, we start off by doing a quick switcheroo on the variables in order to get the inverse of any expression.

$\bf \stackrel{f(x)}{y}=\cfrac{x-1}{2}\implies \stackrel{switcheroo}{x=\cfrac{y-1}{2}}\implies 2x=y-1\implies 2x+1=\stackrel{f^{-1}(x)}{y} \\\\\\ 2(5)+1=^{-1}(5)\implies 11=f^{-1}(5)$

Answer 2

Answer:

11

Step-by-step explanation:

To find the inverse let y = f(x) and rearrange making x the subject, that is

y = $\frac{x-1}{2}$ ( multiply both sides by 2 )

2y = x - 1 ( add 1 to both sides )

2y + 1 = x

Change y back into terms of x, thus

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

$f^{-1}$(5) = 2(5) + 1 = 10 + 1 = 11