Question

Let h(x) = (g o f)(x) = sqrt{x+3}

Which of the following could be a possible decomposition of h(x )?

Answer 1

The answer is f(x)=x+3; g(x)=sqrt x

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Explanation:

Answer 2

I am assuming you meant to write the following options

A. f(x)=x+3; g(x)=√x
B. f(x)=x; g(x)=x+3
C. f(x)=√x; g(x)=x+3
D. f(x)=3x; g(x)=√x

You need to find a fucntion f(x) that once evaluated in g(x) gives us as a result h(x)

h(x) = g(f(x))

Looking at the options, the answer is A.

g(f(x)) = sqrt(f(x)) = sqrt (x + 3) = h(x)