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Hey I got couple of function type questions I need you to show me how to do?

1.f(x)={x^2 if x<0

f(x)={x+1 if x≥0

Find f(-2), f(-1), f(0), f(1), f(2)

2. f(x)=x^2-9 and g(x)=√(9-x^2)

Find (fog)(x) and (gof)(x)

1. For this question, the only condition is if x >= 0 or x < 0.

For x=-2 and x=-1, x<0, so the answer is the first part of the function.

That is, it is x², and that gives f(-2) = 4 and f(-1) = 1.

For x=0, x=1, and x=2, we get f(x) = x+1, so the answers are

f(0) = 1, f(1) = 2, and f(2) = 3.

2. Isn't (fog)(x) the same as f(g(x))?

That means (gof)(x) would be the same as g(f(x)).

If g(x) = √(9-x²), so putting this into f(x) = g²(x) - 9 as g(x) gives f(g(x)) = 9-x² - 9.

The 9's cancel, giving f(g(x)) = -x².

That also means that (gof)(x) would be the same as g(f(x)).

Since f(x) = x²-9, this gives g(f(x)) = √(9-(x²-9)²).

In this case, that's all the farther we can go.

Algebra

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