Practice Function Composition in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Function composition applies one function to the output of another: (f \circ g)(x) = f(g(x)), meaning evaluate g first, then apply f to the result.
Chain two machines together—output of the first goes into the second.
Example 1
easyGiven f(x) = 2x + 1 and g(x) = x^2, find (f \circ g)(3).
Example 2
mediumGiven f(x) = x + 3 and g(x) = 2x^2 - 1, find the formula for (g \circ f)(x).
Example 3
easyGiven f(x) = x - 4 and g(x) = 3x, find (f \circ g)(5).
Example 4
hardGiven f(x) = \sqrt{x} and g(x) = x^2 + 5, find the domain of (f \circ g)(x).