Finding Inputs of Functions Revision Notes for Leaving Cert Mathematics

Finding Inputs of Functions

We've seen how to evaluate functions. That is, we derived an output from a given input. But what if we wanted to go backwards ? That is, from a given output, can we determine what that input was ?

Finding inputs for a function involves determining the values of the independent variable (usually $x$ that satisfy certain conditions. These conditions could be based on the output of the function or the function's domain.

Example

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Given the function $f(x)=2x+3$ , find the input ( $x$ ) when the output is 11.

We know that output has to be 11, but $f(x)$ represents the output too.

f(x)=11

Instead of $f(x)$ , we can write the expression that $f(x)$ represents.

2x+3=11

Now, you can solve for the expression :

2x=8

x=4

The original input that yielded $f(x)=11$ was x=4. You may verify your answer by substituting back into the original function.

f(4)=2(4)+3=11

Finding Inputs of Functions (Leaving Cert Mathematics): Revision Notes