Inverse Function Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Find the inverse of f(x)=x4+2f(x) = \frac{x}{4} + 2.

Solution

  1. 1
    Swap: x=y4+2x = \frac{y}{4} + 2. Subtract 2: x−2=y4x - 2 = \frac{y}{4}.
  2. 2
    Multiply by 4: y=4(x−2)=4x−8y = 4(x - 2) = 4x - 8.

Answer

f−1(x)=4x−8f^{-1}(x) = 4x - 8
Linear functions always have linear inverses. The operations are reversed in opposite order.

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 1 easy

Find the inverse of [formula].

Example 2 medium

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

Example 4 hard

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

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