What is the inverse of f:x=x+2/3

Mathematics

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Step-by-step solution

4 steps

To find the inverse of the function f(x)=x+23f(x) = x + \frac{2}{3}, follow these steps:

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

    y=x+23y = x + \frac{2}{3}

  2. Swap xx and yy in the equation.

    x=y+23x = y + \frac{2}{3}

  3. Solve the new equation for yy.

    To isolate yy, subtract 23\frac{2}{3} from both sides of the equation.

    x−23=yx - \frac{2}{3} = y y=x−23y = x - \frac{2}{3}

  4. Replace yy with f−1(x)f^{-1}(x) to denote the inverse function.

    f−1(x)=x−23f^{-1}(x) = x - \frac{2}{3}

    The inverse of f(x)=x+23f(x) = x + \frac{2}{3} is \boxed{\textbf{f^{-1}(x) = x - \frac{2}{3}}}.

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