Function Composition and Evaluation

Function composition is the process of applying one function to the results of another function. If $$f(x)$$ and $$g(x)$$ are two functions, then the composition of $$f$$ and $$g$$ is denoted as $$f(g(x))$$ .

The notation for function composition is $$f(g(x))$$ , which means 'apply function g to x, then apply function f to the result of g(x).'.

$$f(3) = 2(3) = 6$$ .

$$g(2) = 2(2^2) - 1 = 8 - 1 = 7$$ .

$$f(-2) = 2(-2) = -4; g(-4) = 2(-4)^2 - 1 = 32 - 1 = 31$$ .

$$f(0) = 2(0) = 0; f(f(0)) = f(0) = 2(0) = 0$$ .

$$f(-1) = 2(-1) = -2; g(-2) = 2(-2)^2 - 1 = 8 - 1 = 7$$ .

$$f(1) = 2(1) = 2$$ .

$$g(0) = 2(0)^2 - 1 = 0 - 1 = -1$$ .

$$g(3) = 2(3^2) - 1 = 18 - 1 = 17; f(17) = 2(17) = 34$$ .