QuestionFind $(f \circ g)(x)$ and $(g \circ f)(x)$ and the domain of each. $$f(x)=x+3, g(x)=2 x^{2}-5 x-3$$ $(f \circ g)(x)=$ $\square$ (Simplify your answer.)
The domain of $(f \circ g)(x)$ is $\square$ . (Type your answer in interval notation.) $(g \circ f)(x)=$ $\square$ (Simplify your answer.)
The domain of $(g \circ f)(x)$ is $\square$ . (Type your answer in interval notation.)

Studdy Solution
The domain of $(g \circ f)(x)$ is determined by the domain of $f(x)$ since $g(x) = 2x^2 - 5x - 3$ is defined for all real numbers. The function $f(x) = x + 3$ is defined for all real numbers.
Thus, the domain of $(g \circ f)(x)$ is:
$$(-\infty, \infty)$$
The simplified expressions and domains are: - $(f \circ g)(x) = 2x^2 - 5x$ - The domain of $(f \circ g)(x)$ is $(-\infty, \infty)$. - $(g \circ f)(x) = 2x^2 + 7x$ - The domain of $(g \circ f)(x)$ is $(-\infty, \infty)$.