Find g(f(x))

Problem

ƒ(x)=√(,2*x+4),g(x)=√(,9*x−16), find *g*(ƒ(x))

Solution

1. Identify the outer function g(x) and the inner function ƒ(x)

2. Substitute the expression for ƒ(x) into every instance of x within the function g(x)

g*(ƒ(x))=√(,9*(ƒ(x))−16)

3. Replace ƒ(x) with its algebraic definition √(,2*x+4)

g*(ƒ(x))=√(,9√(,2*x+4)−16)

Final Answer

g*(ƒ(x))=√(,9√(,2*x+4)−16)

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