Question

I need help this is something from khan academy

Answer 1

Answer: 16

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Step-by-step explanation:

This is a piecewise function. As the name implies, the g(x) is broken up into 3 pieces. Each piece depends on what the input x is.

If x is between
`-\infty` and
`-7`, excluding both endpoints, then we pick the first piece. So in this case,
`g(x) = x^2-5`

Or if
`-7 \le x \le 2`, then we go for the second piece and
`g(x) = 9x-17`

Lastly, if x is between
`2` and
`\infty`, then we go for the last piece and say
`g(x) = (x+1)(x-5)`

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To paraphrase that last section, we have g(x) defined as having a split personality or multiple identities depending on what x is.

• If x is between negative infinity and -7 (exclusive), then g(x) = x^2-5
• If x is between -7 and 2, then g(x) = 9x-17
• If x is between 2 and infinity, then g(x) = (x+1)(x-5)

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The question is: which piece do we pick?

Well, g(7) means that x = 7 for g(x). We'll pick the third piece because 7 is between 2 and infinity. In other words, x = 7 makes
`x > 2` a true inequality.

So,

`g(x) = (x+1)(x-5) \ \text{ when } x > 2\\\\g(7) = (7+1)(7-5) \ \text{ replace every x with 7}\\\\g(7) = (8)(2)\\\\g(7) = 16\\\\`