1 Answer

Kamran Bigdely · Answer 1 · 2023-08-17T09:35:54+0000

$g(f(\text{x})) = -3\text{x}^2+3$

g(f(2)) = -9

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Step-by-step explanation:

Let's compute g(f(x))

We do this by starting with the outer function g(x). Then replace every x with f(x). Then plug in the definition of f(x) as shown below.

$g(\text{x}) = \text{x}-1\\\\g(f(\text{x})) = f(\text{x})-1\\\\g(f(\text{x})) = 4-3\text{x}^2-1\\\\g(f(\text{x})) = -3\text{x}^2+3\\\\$

At this point, we then plug in x = 2 so we can find that...

$g(f(\text{x})) = -3\text{x}^2+3\\\\g(f(2)) = -3(2)^2+3\\\\g(f(2)) = -3(4)+3\\\\g(f(2)) = -12+3\\\\g(f(2)) = -9\\\\$

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