What's the identity inverse of f(x)=3−2x

Mathematics

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Answer

f−1(x)=3−x2f^{-1}(x) = \frac{3 - x}{2}

Graph of f(x) = 3 − 2x

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Key points of f(x) = 3 − 2x
Pointxy
y-intercept03
x-intercept1.50

Step-by-step solution

4 steps

Here's how to find the inverse function for f(x)=3−2xf(x) = 3 - 2x:

  1. Replace f(x)f(x) with yy.

    y=3−2xy = 3 - 2x

  2. Swap xx and yy.

    x=3−2yx = 3 - 2y

  3. Solve for yy.

    Subtract 3 from both sides:

    x−3=−2yx - 3 = -2y

    Divide both sides by -2:

    x−3−2=y\frac{x - 3}{-2} = y y=3−x2y = \frac{3 - x}{2}

  4. Replace yy with f−1(x)f^{-1}(x).

    f−1(x)=3−x2f^{-1}(x) = \frac{3 - x}{2}
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