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Zarrin [17]
3 years ago
6

I. Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x2 + 1. Compute the following: 1. f(g(-1))

Mathematics
1 answer:
aleksandrvk [35]3 years ago
3 0
F(g(-1))
g(-1) = 3(-1) = -3
f(-3) = 2(-3) -1 = -6 -1 = -7
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Answer:

The answer is the letter B.

The first column represents the x-values, and the second row represents the y-values.

For that reason, if we have:

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Then, the matrix will be given by:

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Then, the third colum will be the equality:

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So the correct option is the letter B.

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3 years ago
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Fed [463]

By definition of tangent,

tan(A + B) = sin(A + B) / cos(A + B)

Using the angle sum identities for sine and cosine,

sin(x + y) = sin(x) cos(y) + cos(x) sin(y)

cos(x + y) = cos(x) cos(y) - sin(x) sin(y)

yields

tan(A + B) = (sin(A) cos(B) + cos(A) sin(B)) / (cos(A) cos(B) - sin(A) sin(B))

Multiplying the right side by 1/(cos(A) cos(B)) uniformly gives

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Since 2 tan(A) = 3 tan(B), it follows that

tan(A + B) = (3/2 tan(B) + tan(B)) / (1 - 3/2 tan²(B))

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Putting everything back in terms of sin and cos gives

tan(A + B) = (5 sin(B)/cos(B)) / (2 - 3 sin²(B)/cos²(B))

Multiplying uniformly by cos²(B) gives

tan(A + B) = 5 sin(B) cos(B) / (2 cos²(B) - 3 sin²(B))

Recall the double angle identities for sin and cos:

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

cos(2x) = cos²(x) - sin²(x)

and multiplying uniformly by 2, we find that

tan(A + B) = 10 sin(B) cos(B) / (4 cos²(B) - 6 sin²(B))

… = 10 sin(B) cos(B) / (4 (cos²(B) - sin²(B)) - 2 sin²(B))

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The Pythagorean identity,

cos²(x) + sin²(x) = 1

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so it follows that

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… = 5 sin(2B) / (4 cos(2B) - 1)

as required.

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Answer:

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Answer:

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Step-by-step explanation:

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