Composition and inverses of functions

In summary, a composition of functions is a mathematical operation that combines two or more functions to create a new function by using the output of one function as the input of another. To find the composition of two functions, you substitute the input of the inner function into the outer function and simplify the resulting expression. An inverse function is a function that undoes the original function by swapping the input and output values. To find the inverse of a function, you switch the positions of the input and output variables and solve for the output variable. However, not every function has an inverse as it must pass the horizontal line test.
  • #1
unknownuser
2
0
just started my precalculus class and i can not understand what's going on and its makes me mad too. In our book we are on 1-2 Composition and Inverses of Functions like for this one problem:

Find [f of g] (x) and [g of f] (x).
1. f(x)= 1/2x-7
g(x)= x=6



and this problem

f(x)=3x^2 and g(x)=x-4 please help
 
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  • #2
Stop shouting.
 
  • #3
And why would you put a thread title "Precalculus" in the "Calculus & Beyond" section instead of in the section called "Precalculus Mathematics"?
 

FAQ: Composition and inverses of functions

What is a composition of functions?

A composition of functions is a mathematical operation that combines two or more functions to create a new function. The output of one function becomes the input of another function.

How do you find the composition of two functions?

To find the composition of two functions, you need to substitute the input of the inner function into the outer function. In other words, the output of the inner function becomes the input of the outer function. You can then simplify the resulting expression to get the final composition of the two functions.

What is an inverse function?

An inverse function is a function that "undoes" the original function. It swaps the input and output values of the original function, meaning that the output of the original function becomes the input of the inverse function.

How do you find the inverse of a function?

To find the inverse of a function, you need to switch the positions of the input and output variables and then solve for the output variable. This resulting function is the inverse of the original function.

Can every function have an inverse?

No, not every function has an inverse. For a function to have an inverse, it must pass the horizontal line test, meaning that any horizontal line drawn on the graph of the function only intersects the graph at most once. If a function does not pass this test, it does not have an inverse.

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