What is the inverse of the function [tex]f(x)=x+3[/tex]?

Replace f ( x ) with y : y = x + 3 .
Swap x and y : x = y + 3 .
Solve for y : y = x − 3 .
The inverse function is x − 3 ​ .

Explanation

Understanding the Problem We are given the function f ( x ) = x + 3 and we want to find its inverse. The inverse function, denoted as f − 1 ( x ) , is a function that 'undoes' the original function. In other words, if we apply f to some value x and then apply f − 1 to the result, we should get back the original value x .

Finding the Inverse Function To find the inverse of the function f ( x ) = x + 3 , we can follow these steps:

Replace f ( x ) with y : y = x + 3 .

Swap x and y : x = y + 3 .

Solve for y in terms of x : y = x − 3 .

Replace y with f − 1 ( x ) : f − 1 ( x ) = x − 3 .

The Answer Therefore, the inverse of the function f ( x ) = x + 3 is f − 1 ( x ) = x − 3 . Comparing this with the given options, we see that the correct answer is h ( x ) = x − 3 .


Examples
Imagine you're baking a cake and you need to convert Celsius to Fahrenheit. The formula to convert Celsius (C) to Fahrenheit (F) is a function: F = f ( C ) = 5 9 ​ C + 32 . If you know the Fahrenheit temperature and want to find the Celsius temperature, you need to find the inverse function. The inverse function would be C = f − 1 ( F ) = 9 5 ​ ( F − 32 ) . This allows you to easily convert back from Fahrenheit to Celsius, just like finding the inverse of a mathematical function.

Answered by GinnyAnswer | 2025-07-03

The inverse of the function f ( x ) = x + 3 is f − 1 ( x ) = x − 3 . This means that for every output from the original function, you can apply the inverse to get back the input. In short, f − 1 ( x ) undoes the effect of f ( x ) .
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Answered by Anonymous | 2025-07-04