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Composition of Functions

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Composition of Functions, a selection of answers from the Dr. Math archives.

Why Do We Have Functions?
Why do we have functions? Why do we have things like (g(x) = x + 3, find g[f(2)] ?

Composite Functions
My students can't understand composite functions.

Composition of Functions
How do I find f(g(x)) if f(x) = x+2 and g(x) = 3x-1?

Evaluating Composite Functions
If f(x) = 3, and g(x) = x^2 + 1 divided by the square root of (x^2 -1), how do you evaluate the composite function of f composed with g (f circle g)?

Composing Functions
I'm trying to find f-of-g where f(x) = 2x and g(x) = 3x^2 + 1. What happens when you compose two functions?

Domain of a Composite Function
I don't completely understand how to find the domain of a composite function. Could you please explain it?

Composition Functions with Added x Value
If x = 1, evaluate g(f(f(x))). I'm confused with this added value of x = 1.

Composite Functions Using Logarithms
Suppose f and g are functions defined by f(x)=x+2 and g(x)=x. Find all x>-2 for which: 3^[g(x)*logbase3 f(x)]=f(x).

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