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Numerade Educator

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Problem 40 Medium Difficulty

Find $ f \circ g \circ h $.

$ f(x) = \mid x - 4 \mid $ , $ g(x) = 2^x $ , $ h(x) = \sqrt{x} $

Answer

$\left|2^{\sqrt{x}}-4\right|$

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Video Transcript

here we have functions F, g and H, and we want to find f of g of h. Another way to write that is like this with parentheses, f of G of H and when we write it that way we can see that the inside most function is h of X. So we're going to take a chav X, and we're going to substitute in two G of X, so that gives us G of h of X. So G of h of X is going to be two to the power of square root. X now G of h of X gets substituted in two f of X. So we're going to take that whole thing that we just found and substituted in two F of X, and that's going to give us the absolute value of two to the square root X minus four