Question

(a) find the inverse function of f(x)=9x - 6. f^(-1)(x)= (b) the graphs of f and f^(-1) are symmetric with respect to the line defined by y = question help: video submit question

Explanation:

Step1: Set $y = f(x)$

Let $y=9x - 6$.

Step2: Solve for $x$ in terms of $y$

Add 6 to both sides: $y + 6=9x$. Then divide by 9: $x=\frac{y + 6}{9}$.

Step3: Replace $x$ with $f^{-1}(x)$ and $y$ with $x$

$f^{-1}(x)=\frac{x + 6}{9}$.

Step4: Recall symmetry property

The graphs of a function $f(x)$ and its inverse $f^{-1}(x)$ are symmetric with respect to the line $y = x$.

Answer:

(a) $f^{-1}(x)=\frac{x + 6}{9}$
(b) $x$