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

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

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Solution Steps

Step 1: Replace f(x) with y

Given a linear function f(x)=3x2f(x) = 3_x - 2, we start by replacing f(x)f(x) with yy, resulting in the equation y=3x2y = 3_x - 2.

Step 2: Swap x and y

To find the inverse function, we swap xx and yy in the equation, leading to x=3y2x = 3*y - 2.

Step 3: Solve the equation for y

We isolate yy on one side of the equation by first subtracting bb from both sides, resulting in x+2=3yx + 2 = 3*y. Then, we divide both sides by aa to get x+23=y\frac{x + 2}{3} = y.

Step 4: Express the inverse function

Finally, we replace yy with f1(x)f^{-1}(x) to express the inverse function in terms of xx: f1(x)=xbaf^{-1}(x) = \frac{x - b}{a}, which simplifies to f1(x)=x/3+2/3f^{-1}(x) = x/3 + 2/3.

Final Answer:

The inverse function of f(x)=3x2f(x) = 3*x - 2 is f1(x)=x/3+2/3f^{-1}(x) = x/3 + 2/3.

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