Question

Im confused on this one

Answer 1

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;

(-∞,∞)

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: (-∞,∞)