Question

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)

Answer 1

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 = (-∞, ∞)