Ask Dr. Math 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).