Question

im confused on this one

Answer 1

Answer:

The first choice is correct;

(-∞,∞)

Step-by-step 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;

(-∞,∞)

Answer 2

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: (-∞,∞)