If f(x) = x2 – 1 and g(x) = 2x – 3, what is the domain of (f circle g) (x)? (negative infinity, infinity) Left-bracket negative
1, infinity) Left-bracket negative 5, infinity) (infinity, negative infinity)
1 answer:
Answer:
A. (-∞, ∞)
Step-by-step 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 = (-∞, ∞)
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Answer:
Step-by-step explanation:
Method #1
We can draw a <em>right triangle</em> on the graph upon where the points are located and use the Pythagorean Theorem:
* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.
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Method #2
We can use the Distance Formula:
<em>N</em>[−3, 2] <em>M</em>[−6, 0]
* Whenever we talk about distance, we ONLY want the NON-NEGATIVE root.
** You see? It does not matter which method you choose, as long as you are doing the work correctly.
I am delighted to assist you anytime.