Im confused on this one

Question

asked Feb 6, 2020 64.5k views

2 Answers

Marcelo Glasberg · Answer 1 · 2020-02-09T08:03:32+0000

Answer:

The first choice is correct;

(-∞,∞)

Explanation:

We have been given the following functions;

$f(x)=x^(2)-1\\\\g(x)=2x-3$

We are to determine the domain of (fog)(x).

The composite function, (fog)(x) is obtained by substituting g(x) in place of x in the function f(x);

(fog)(x) = f[g(x)] =
(2x-3)^(2)-1

Clearly the function will be defined everywhere on the number line since it has no undefined points or domain constraints. The domain is thus;

(-∞,∞)

Eliot Ball · Answer 2 · 2020-02-10T21:56:44+0000

For this case we have the following functions:

$f (x) = x ^ 2-1\\g (x) = 2x-3$

We must find
$(f_ {0} g) (x):$

By definition of composite functions we have to:

$(f_ {0} g) (x) = f (g (x))$

So:

$(f_ {0} g) (x) = (2x-3) ^ 2-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 9-1\\(f_ {0} g) (x) = 4x ^ 2-12x + 8$

The domain of the function is given by all the values for which the function is defined.

The function is defined for all real numbers.

Answer:

Domain: (-∞,∞)