Question

Assume the domain of f and f^-1 is (-infinity,infinity). Solve the equation for t:
f((1-2t)/(1+2t)) = 7 ; f^-1 (7) =-3

Answer 1

\[
f^{-1}(f(x)) =x
\]

Answer 2

Let \[
x=\frac{1-2t}{1+2t}
\]

Answer 3

\[
f(x) = 7
\]take \(f^{-1}\) of both sides and get: \[
x = f^{-1}(7) = -3
\]

Answer 4

And so \[
x=-3\implies \frac{1-2t}{1+2t} = -3
\]

Answer 5

Can you solve for \(t\) now?

Answer 6

Yes thank you!