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Inverse functions worksheets Grade 10

Find the inverse of a function by swapping x and y and solving for y.

The front of the free inverse functions worksheet
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Free · Worked example · 7 problems · Answer key · US Letter

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How to do it

Write y for f(x), swap x and y, and solve for y. The answer is f⁻¹(x).

f(x)=x3+9→f−1(x)=x−93f(x) = x^{3} + 9\quad \to \quad f^{-1}(x) = \sqrt[3]{x - 9}
y=x3+9y = x^{3} + 9write y for f(x)
x=y3+9x = y^{3} + 9swap x and y
x−9=y3x - 9 = y^{3}subtract 9
f−1(x)=x−93f^{-1}(x) = \sqrt[3]{x - 9}solve for y

Example problems

  1. f(x)=4x+63→f(x) = \dfrac{4x + 6}{3}\quad \to \quad
  2. f(x)=5x+13→f(x) = \dfrac{5x + 1}{3}\quad \to \quad
  3. f(x)=x−7x−5→f(x) = \dfrac{x - 7}{x - 5}\quad \to \quad
  4. f(x)=5x−14→f(x) = \dfrac{5x - 1}{4}\quad \to \quad

Functions

  1. Evaluating functions
  2. Finding the domain of a function
  3. Adding, subtracting and multiplying functions
  4. Composition of functions
  5. Inverse functions
  6. Transformations of functions
  7. Even and odd functions
  8. Average rate of change