Practice Function Notation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Function notation f(x) is a shorthand that names a function (f) and specifies its input (x). Writing f(3)=10 means that when the input is 3, the function produces the output 10. This notation is not multiplication.

The notation f(x) is not "f times x" — it means "the output of function f when the input is x." The parentheses contain the input, not a multiplication.

Showing a random 20 of 50 problems.

Example 1

medium
If f(x)=x2−4x, find all x with f(x)=0.

Example 2

medium
If f(x)=x2, compute f(a)−f(b) in factored form.

Example 3

challenge
A function satisfies f(xy)=f(x)+f(y) for all positive x,y and f(2)=1. Find f(8).

Example 4

challenge
If f(x)=xx+1, simplify f(f(x)).

Example 5

medium
If f(x)=2x−1 and g(x)=x2+3, find (f∘g)(x) and (g∘f)(x).

Example 6

easy
If f(x)=2x, find f(−3).

Example 7

easy
If f(x)=x+1, find f(a).

Example 8

medium
If f(x)=2x+1 and g(x)=x2, find f(g(2)).

Example 9

medium
If f(x)=x2−3x, find f(x−2) and simplify.

Example 10

hard
If f(x)=2x+5, find f−1(x) (the inverse).

Example 11

medium
If f(x)=x+3x−5, list all x where f is undefined.

Example 12

medium
If f(x)=4x−1, find f(2x).

Example 13

medium
If f(x)=∣x∣, find f(−5)+f(5).

Example 14

easy
If f(x)=3x2−2x+1, find f(−2).

Example 15

easy
If f(x)=5, find f(100).

Example 16

hard
If f(x)=1x for x≠0, simplify f(x+h)−f(x)h.

Example 17

medium
If f(x)=5x−3 and f(c)=22, find c.

Example 18

easy
If f(x)=−x+4, find f(−2).

Example 19

easy
If f(x)=x2, find f(0).

Example 20

medium
If f(x)=3x+2 and g(x)=x−1, find g(f(1)).
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