Answer
$a.\quad 40,44,52,60$
$ b.\quad$Yes, $\displaystyle \quad f^{-1}(x)=\frac{1}{2}x-12$
$c.\quad 8,10,14,18$
Work Step by Step
$ a.\quad$
$f(8)=2(8+12)=2(20)=40$
$f(10)=2(10+12)=2(22)=44$
$f(14)=2(14+12)=2(26)=52$
$f(18)=2(18+12)=2(30)=60$
$ b.\quad$
$f(x)=2x+24$
is a linear function, not constant, so its graph is an oblique line that passes the horizontal line test.
It is one-to-one and has an inverse.
To find a formula for the inverse,
1. Replace $f(x)$ with $y.$
$y=2x+24$
2. Interchange $x$ and $y$. (This gives the inverse function.)
$x=2y+24$
3. Solve for $y.$
... subtract 24,
$ x-24=2y,\qquad$ ... divide with 2
$\displaystyle \frac{1}{2}x-12=y $
4. Replace $y$ with $f^{-1}(x)$ . (This is inverse function notation.)
$f^{-1}(x)=\displaystyle \frac{1}{2}x-12$
$ c.\quad$
$f^{-1}(40)=\displaystyle \frac{1}{2}(40)-12=8$
$f^{-1}(44)=\displaystyle \frac{1}{2}(44)-12=10$
$f^{-1}(52)=\displaystyle \frac{1}{2}(52)-12=14$
$f^{-1}(60)=\displaystyle \frac{1}{2}(60)-12=18$
