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2 votes
If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain of (f circle g) (x)?

User Molf
by
4.6k points

1 Answer

3 votes

Answer:

(-∞, ∞)

Explanation:

f circle g (x) is another way of expressing f(g(x)). Basically, we have to plug g(x) into f(x) wherever we see x's.

f(x) = x^2 - 1

f(x) = (2x-3)^2 - 1

Now find the domain. I think the easiest way to do this is to graph it. I've attached the graph. You can also do it algebraically by thinking about it: it's a positive parabola (+x^2) and its minimum is -1, so its range will not be all real numbers, but its domain will certainly be. (The range would be answer choice B!)

Domain = (-∞, ∞)

User Joslyn
by
5.2k points
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