Functions and Function Notation

Method

Finding the Input of a Function

Given a function, it is possible to find the input that produces a certain output. This is done by substituting the given output value for the dependent variable and then solving for the independent variable. For the following function, try finding the x-value for which f(x)=21. f(x)=4x-3 To find the input that produces a certain output, there are two steps to follow.

1
Substitute the Output for f(x)
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Start by substituting the given output value for f(x). In this case, it means substituting 21 for f(x).

f(x)=4x-3
21=4x-3

2
Solve for x
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After that, solve the resulting equation for x.

21 = 4x-3
24 = 4x
6 = x
x=6

As shown, f(x) is equal to 21 when x=6.

Exercises
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