QuestionLet $f(x)=-3 x+4$. Then $$f^{-1}(x)=$$

Studdy Solution
Verify the inverse function by checking if $f(f^{-1}(x)) = x$ and $f^{-1}(f(x)) = x$.
First, check $f(f^{-1}(x))$:
$$f\left(-\frac{x}{3} + \frac{4}{3}\right) = -3\left(-\frac{x}{3} + \frac{4}{3}\right) + 4$$
Simplify:
$$= x - 4 + 4 = x$$
Now, check $f^{-1}(f(x))$:
$$f^{-1}(-3x + 4) = -\frac{-3x + 4}{3} + \frac{4}{3}$$
Simplify:
$$= x$$
Both conditions are satisfied, confirming that the inverse function is correct.