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Gennadij [26K]
3 years ago
14

If f(x)= -x^2 - 1, and g(x)=x + 5, then g(f(x))=___x^2+___x+___​

Mathematics
1 answer:
alekssr [168]3 years ago
4 0

Answer:

Step-by-step explanation:

g(f(x))

g(-x^2 - 1)

-x^2 + 0x + 4= -x^2 + 4

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Simplify using trigonometric identities<br> 2sinθ - sin2θ cosθ
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Double angle identity for sine:

\sin(2x) = 2 \sin(x) \cos(x)

\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)

Factorize the left side.

2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)

Pythagorean identity:

\cos^2(x) + \sin^2(x) = 1

\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)

so that

\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}

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Describe how you would graph a figure that is translated by (x - 4,4+2).
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