Question

f(x) = x^3 + 2x + 6 if A)f^ −1(6) B) f −1(3)

Answer 1

\[f(0)=6\implies f^{-1}(6)=0\]

Answer 2

so we have
\[\text{ if } f^{-1}(3)=t => f(t)=3\]
so this means we need to solve f(t)=3 for t
\[t^3+2t+6=3\]
\[t^3+2t+6-3=0\]
\[t^3+2t+3=0\]
We can guess a solution
how about t=-1
-1-2+3=0 So yes!
t=-3=>f(-3)=3 => \[f^{-1}(3)=-3\]

Answer 3

oops t=-1*

Answer 4

\[t=-1=>f(-1)=3=>f^{-1}(3)=-1*\]

Answer 5

perfect thnk you so much ery good explantation as well :)