Hi, I have a quick question about inverse functions.

Thread starter Faith S
Start date Aug 28, 2018
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Functions Hi Inverse Inverse functions Precalculus

In summary, an inverse function is a function that undoes the action of another function. To find the inverse of a function, you can swap the x and y variables and solve for y. The notation for inverse functions is f<sup>-1</sup>(x) and not all functions have an inverse. Inverse functions are useful for solving equations and understanding relationships between quantities, and are used in various fields such as engineering, physics, and computer science.

Aug 28, 2018

Faith S

One of our homework problem asks:

If f is a one-to-one function such that f(-3)=5 , find x given that f^-1 (5)=3x-1.

Here's how I attempted to solve the problem:
-3=3x-1
3x=-2
x=-2/3

Is this the correct way to solve the problem?

Last edited: Aug 28, 2018

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Aug 28, 2018

Cutter Ketch

Yes

What is an inverse function?

An inverse function is a function that undoes the action of another function. It is like the "opposite" of a function, and when the two are composed, they cancel each other out.

How do you find the inverse of a function?

To find the inverse of a function, you can follow these steps: 1) Write the original function in the form of y = f(x) 2) Swap the x and y variables, so that you have x = f(y) 3) Solve for y to find the inverse function.

What is the notation for inverse functions?

The notation for inverse functions is f^-1(x). This is read as "f inverse of x".

Can any function have an inverse?

No, not all functions have an inverse. For a function to have an inverse, it must be a one-to-one function, meaning that each input has only one unique output. If there are multiple inputs with the same output, the function does not have an inverse.

How are inverse functions useful?

Inverse functions are useful for solving equations and understanding relationships between two quantities. They are also used in fields such as engineering, physics, and computer science.