Given g(x) = 5x^2 - 4xg(x)=5x2−4x and h(x) =sqrt(x - 7)h(x)=√x−7 how do you find g(h(x))?

1 Answer
Jim G.
Feb 28, 2016

5x - 35 - 4sqrt(x-7) 5x−35−4√x−7

Explanation:

g(h(x)) = g(sqrt(x-7)) g(h(x))=g(√x−7)

Now substitute x = sqrt(x-7) " for x in g(x) "√x−7 for x in g(x)

hence: g(sqrt(x-7)) = 5(sqrt(x-7))^2 - 4(sqrt(x-7)) g(√x−7)=5(√x−7)2−4(√x−7)

now (sqrt(x-7))^2 = x-7 (√x−7)2=x−7

rArr g(h(x)) = 5(x-7) -4(sqrt(x-7)) ⇒g(h(x))=5(x−7)−4(√x−7)

= 5x - 35 - 4(sqrt(x-7))=5x−35−4(√x−7)

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