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

11

Explanation:

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

y =
`(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