if $f(x) = x^2 - 1$ and $g(x) = 2x - 3$, what is the domain of $(f\\circ g)(x)$?\n$(-\\infty,\\infty)$\n$-1,\…

if $f(x) = x^2 - 1$ and $g(x) = 2x - 3$, what is the domain of $(f\\circ g)(x)$?\n$(-\\infty,\\infty)$\n$-1,\\infty)$\n$-5,\\infty)$\n$(\\infty,-\\infty)$

if $f(x) = x^2 - 1$ and $g(x) = 2x - 3$, what is the domain of $(f\\circ g)(x)$?\n$(-\\infty,\\infty)$\n$-1,\\infty)$\n$-5,\\infty)$\n$(\\infty,-\\infty)$

Answer

Explanation:

Step1: Find composite function $(f\circ g)(x)$

Substitute $g(x)$ into $f(x)$: $$(f\circ g)(x) = f(g(x)) = (2x-3)^2 - 1$$ Expand and simplify: $$(2x-3)^2 - 1 = 4x^2 -12x +9 -1 = 4x^2 -12x +8$$

Step2: Analyze domain of the function

The resulting function is a polynomial. Polynomial functions are defined for all real numbers.

Answer:

$(-\infty,\infty)$