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### Course: Algebra 1 > Unit 8

Lesson 13: Intro to inverse functions# Functions: FAQ

Frequently asked questions about functions

## What is a function?

A function is a mathematical rule that matches inputs to outputs. We can think of it like a machine: put a number in, the machine does some calculations, and out pops a corresponding number.

Inputs and outputs don't have to be numbers. Functions themselves can be inputs and outputs.

Learn more with our What is a function video.

## Where do we use the topics from this unit in the real world?

Functions are used in all sorts of real-world applications! For example, we use functions to model physical processes, like the motion of a car or the growth of a population. We can also use them to analyze data, like finding the rate of change of a company's profits over time.

Practice with our Graph interpretation word problems exercise.

## What's the difference between the domain and range of a function?

The domain is the set of all possible inputs that the function can take, while the range is the set of all outputs the function can produce.

Practice with our Domain and range from graph exercise.

## How do we determine if a given relationship is a function?

To be a function, every input must correspond to exactly one output. If we find an input that has two different outputs, then we know that the relationship is not a function.

Practice with our Recognize functions from graphs exercise.

Practice with our Recognize functions from tables exercise.

## How do we use function notation?

Function notation is a shorthand way of expressing a function. Instead of writing out the equation every time, we can use a letter (usually $f$ ) to represent the function, and write $f(x)$ to indicate that we are plugging in the value $x$ as the input.

Practice with our Function notation word problems exercise.

## What's the difference between absolute and relative maxima and minima points?

An absolute maximum or minimum is the highest or lowest point on the entire function. A relative maximum or minimum is the highest or lowest point within a given interval, but not necessarily the entire function. These points can be important for understanding the behavior of a function.

Practice with our Relative maxima and minima exercise.

Practice with our Absolute maxima and minima exercise.

## What does it mean when we say a function is increasing or decreasing?

A function is increasing over an interval if the outputs get larger as the inputs increase. A function is decreasing if the outputs get smaller as the inputs increase.

Practice with our Increasing and decreasing intervals exercise.

## What is the average rate of change?

The average rate of change is a measure of how much a function changes over a given interval. To calculate it, we divide the change in output by the change in input.

Practice with our Average rate of change: graphs & tables
exercise.

## What are inverse functions?

Inverse functions are functions that "undo" each other. If we plug the output of one function into the inverse function, we get back the original input.

Practice with our Evaluate inverse functions exercise.

Practice with our Finding inverses of linear functions exercise.

## Want to join the conversation?

- When is a function an inverse of itself?(9 votes)
- Good question. There are several functions that are their own inverses.

Here are some of them:

f(x)=x

f(x)=-x

f(x)=1/x

You can test to see if a function is its own inverse by taking f(f(x)), or composing the function inside itself. If the answer is x, then it is its own inverse.

Example for f(x)=-x

f(f(x)) = -(-x) = x(13 votes)

- Are inverse functions relevant to the real world?(5 votes)
- Yes, inverse functions are relevant in the real world and find applications in finance, physics, engineering, computer science, medicine, navigation, and statistics. They help model and solve practical problems across various fields. For example, in finance, they help calculate interest rates. If you have a savings account with a known final amount and interest rate, the inverse function allows you to determine the initial investment.(8 votes)

- do we solve for x or y to find the inverse(2 votes)
- To find the inverse swap, x and y, then solve for y again.(3 votes)

- how do you do the ones without parentheses on the finding inverses of linear functions excercise? I got stuck there. HELP?(2 votes)
- If it was something like 8x-2, you still divide by 8, but you also divide -2 by 8 as well.(4 votes)

- How do you find the function of William Micvay.(2 votes)
- What is the square rout of pi(2 votes)
- These simply dont make sense to me(2 votes)
- h −1 (−4) what do these symbols mean(1 vote)
- The function is formated as h(x) so -4 would be the input. as for the -1, it is often used not as an exponent but to represent the inverse or oposite(2 votes)

- What’s the square root of a circle(1 vote)
- The area of a circle is pi r squared(2 votes)

- I cant wait for geometry.... this sucks.(1 vote)