Question

Suppose that the function g is defined, for all real numbers, as follows.

Answer 1

Answers:

• g(-1) = -1
• g(1) = -3/2
• g(5) = -7/2

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Explanation:

The piecewise function g(x) is defined based on what the input is.

• If the input x is less than -2, then g(x) = 2
• Or if $-2 \le x < 1$ then g(x) = -(x-1)^2+3
• Or if $x \ge 1$ then g(x) = (-1/2)x-1

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In the case of g(-1), we have x = -1 which makes $-2 \le x < 1$ true.

So we'll use the second piece

g(x) = -(x-1)^2+3

g(-1) = -(-1-1)^2+3

g(-1) = -(-2)^2+3

g(-1) = -4+3

g(-1) = -1

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For g(1), we have x = 1 which makes $x \ge 1$ true

We'll use the third piece

g(x) = (-1/2)x-1

g(1) = (-1/2)*1 - 1

g(1) = -1/2 - 1

g(1) = -1/2 - 2/2

g(1) = -3/2

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For g(5), we have x = 5 which makes $x \ge 1$ true

g(x) = (-1/2)x-1

g(5) = (-1/2)*5-1

g(5) = -5/2 - 1

g(5) = -5/2 - 2/2

g(5) = -7/2