Inverse Function Math Example 1

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Example 1

easy
Find the inverse of f(x)=3x−7f(x) = 3x - 7.

Solution

  1. 1
    Write y=3x−7y = 3x - 7.
  2. 2
    Swap xx and yy: x=3y−7x = 3y - 7.
  3. 3
    Solve for yy: 3y=x+73y = x + 7, so y=x+73y = \frac{x + 7}{3}.
  4. 4
    Therefore f−1(x)=x+73f^{-1}(x) = \frac{x + 7}{3}.

Answer

f−1(x)=x+73f^{-1}(x) = \frac{x + 7}{3}
To find an inverse, swap input and output then solve for the new output. The inverse 'undoes' the original function: applying ff then f−1f^{-1} returns the original input.

About Inverse Function

The inverse of a function ff is a function f−1f^{-1} that reverses ff: if f(a)=bf(a) = b then f−1(b)=af^{-1}(b) = a. It exists only when ff is one-to-one.

Learn more about Inverse Function →

More Inverse Function Examples

Example 2 medium

Find the inverse of [formula] for [formula].

Example 3 easy

Find the inverse of [formula].

Example 4 hard

If [formula], find [formula]. Then verify by showing that [formula].

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