Hopefully I was able to give you a good overview of what composite functions are, now for some harder examples: We are doing the same thing we did before, but this time, letting the input within g(x) as the value of f(x) or x^2. (you might be familiar with this if you take computer science, we are just assigning a variable to an equation, even though necessarily x doesn't equal to g(x) or 2x)Ģ) Rewriting the question we need to solve and the information we know.ģ) Plugging 2x for the value of x in the function f(x) We aren't saying that whatever we plug into x will be inputted into g(x) and get the same value, we are just saying, that whenever we find the value of x in the function f(x) we will plug in that value into the equation. Just let the equation/variable g(x) inside f(x) equal to the value of x inside x^2 (Ex: if we have t(x)= 2x^2 and said we needed to find t(3) that is just = 2*(3)^2).

This might seem a bit intimidating, but it is quite simple.Just doing the same thing we did with our normal variables and plugging it in. Now, suppose we are told that we have another equation g(x) = 2x. Instead of assigning another number into a variable, you are inputting an equation with another variable.Įx: Suppose we have our quadratic equation, f(x) =x^2. You might be wondering what was the point of that whole explanation, but that is the same way with composite functions.

We can use the same equation but change the value for x.

If we want to find the value for y given that x =5, it's quite simple. We can say that x= 5 and assign these equations to another variable, y.Įx: y = 2x^2 + 2x +1. The variable we have, x is like a folder, it has a certain value/name assigned to it. 3x^2 + 3x + 1, we can use it in a quadratic form, linear x + 3, polynomial x^4 + 3x^2 + 1. We then put those variable into functions, equations, etc to find what we need.Įx: We have the variable x, now we can assign it into any form of a function we want. Usually what we have is we have a variable with a certain value assigned to it.

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