Math Help - [ URGENT ] anyone can help me solve preimage question ?

1. [ URGENT ] anyone can help me solve preimage question ?

Determine the pre-image under f for each of the intervals

(i) [-5, -1]
(ii) [-5, 0]
(iii) [-2, 4]
(iv) (5, 10)
(v) [11, 17]

anyone can write the working down ?

2. Re: [ URGENT ] anyone can help me solve preimage question ?

$f(x)=\begin{cases}x+7, & x\leq0 \\ -2x+5, & 0

Determine the pre-image under f for each of the intervals

(i) [-5, -1]
Ask yourself, over what interval of values for $x$ is $f(x)\in[-5,-1]$?

$f(x) = x+7 = -5 \implies x=-12 \text{ and } f(x)=x+7=-1 \implies x=-8$

$f^{-1}\left([-5,-1]\right) = [-12,-8]$

Thank you