Answer:
C
Step-by-step explanation:
To find the inverse, let y = f(x) then rearrange making x the subject, that is
y = 5(x + 3)³ - 2 ( add 2 to both sides )
y + 2 = 5(x + 3)³ ( divide both sides by 5 )
(x + 3)³ = [tex]\frac{y+2}{5}[/tex]
Take the cube root of both sides
x + 3 = [tex]\sqrt[3]{\frac{y+2}{5} }[/tex]
Subtract 3 from both sides
x = [tex]\sqrt[3]{\frac{y+2}{5} }[/tex] - 3
Change y back into terms of x, so
[tex]f^{-1}[/tex] (x ) = [tex]\sqrt[3]{\frac{x+2}{5} }[/tex] - 3 → C
