Questions: What is the inverse function of f(x)= 3x-2 ?

Transcript text: What is the inverse function of $f(x)=$ $3 x-2 ?$

Solution

Solution Steps

Step 1: Replace f(x) with y

Given a linear function $f(x) = 3_x - 2$, we start by replacing $f(x)$ with $y$, resulting in the equation $y = 3_x - 2$.

Step 2: Swap x and y

To find the inverse function, we swap $x$ and $y$ in the equation, leading to $x = 3*y - 2$.

Step 3: Solve the equation for y

We isolate $y$ on one side of the equation by first subtracting $b$ from both sides, resulting in $x + 2 = 3*y$. Then, we divide both sides by $a$ to get $\frac{x + 2}{3} = y$.

Step 4: Express the inverse function

Finally, we replace $y$ with $f^{-1}(x)$ to express the inverse function in terms of $x$: $f^{-1}(x) = \frac{x - b}{a}$, which simplifies to $f^{-1}(x) = x/3 + 2/3$.

Final Answer:

The inverse function of $f(x) = 3*x - 2$ is $f^{-1}(x) = x/3 + 2/3$.

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