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 backward ? 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

infoNote

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

500K+ Students Use These Powerful Tools to Master Finding Inputs of Functions For their Leaving Cert Exams.

Enhance your understanding with flashcards, quizzes, and exams—designed to help you grasp key concepts, reinforce learning, and master any topic with confidence!

150 flashcards

Flashcards on Finding Inputs of Functions

Revise key concepts with interactive flashcards.

Try Mathematics Flashcards

9 quizzes

Quizzes on Finding Inputs of Functions

Test your knowledge with fun and engaging quizzes.

Try Mathematics Quizzes

29 questions

Exam questions on Finding Inputs of Functions

Boost your confidence with real exam questions.

Try Mathematics Questions