Question

Let g(x) = x² - 3 and h(x) = 2x + 5. Find g(h(x)).

Answer 1

Answer: $4x^2+20x+22$

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Work Shown:

$g(x) = x^2 - 3\\\\g(h(x)) = (h(x))^2 - 3\\\\g(h(x)) = (2x+5)^2 - 3\\\\g(h(x)) = (2x+5)(2x+5) - 3\\\\g(h(x)) = 4x^2+10x+10x+25 - 3\\\\g(h(x)) = 4x^2+20x+25 - 3\\\\g(h(x)) = 4x^2+20x+22$

Explanation: I replaced every x with h(x) in step 2. In step 3, I replaced h(x) with 2x+5 just on the right hand side only. From there, expand and simplify.