Question

question 13
0/10 pts 3 99 details
(a) find the inverse function of f(x)=3x - 2.
f^(-1)(x)=(x + 2)/3
(b) the graphs of f and f^(-1) are symmetric with respect to the line defined by y=
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Explanation:

Step1: Recall inverse - function property

Let $y = f(x)=3x - 2$. To find the inverse, we solve for $x$ in terms of $y$. First, add 2 to both sides: $y + 2=3x$.

Step2: Solve for x

Then divide both sides by 3: $x=\frac{y + 2}{3}$. Swap $x$ and $y$ to get the inverse function $f^{-1}(x)=\frac{x + 2}{3}$.
For part (b), the graphs of a function $y = f(x)$ and its inverse $y = f^{-1}(x)$ are symmetric with respect to the line $y = x$. This is a fundamental property of inverse - functions.

Answer:

(a) $f^{-1}(x)=\frac{x + 2}{3}$
(b) $y = x$