Question

Given the table below, evaluate the following:

a. (f-2g)(2)

b. f(g(-1))

c. g(g(-2))

Please Explain

Answer 1

Part A

See the image labeled "part A". We'll use the values marked in blue and red for f(2) and g(2) respectively. These values are the function outputs when the input is x = 2.

(f-2g)(x) = f(x) - 2*g(x)

(f-2g)(2) = f(2) - 2*g(2)

(f-2g)(2) = 1 - 2*3

(f-2g)(2) = -5

Answer: -5

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Part B

See the image labeled "part B". We'll use the values marked in blue and red for g(-1) and f(0) respectively.

We have to start with g(-1) and then chain it to finding f(0) afterward.

g(-1) = 0

f(g(-1)) = f(0) = 9

Answer: 9

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Part C

See the image labeled "part C". We'll use the values marked in blue and red for g(-2) and g(-3) respectively.

Because g(-2) is the innermost function, it must go first, then g(-3) can go next.

g(-2) = -3

g(g(-2)) = g(-3) = 8

Answer: 8