Chapter 2.1, Problem 11AYU

True or False The domain of $\left(f\circ g\right)\left(x\right)$ consists of the numbers $x$ that are in the domains of both $f$ and $g$.

To determine

True or False.

Answer to Problem 11AYU

False

Explanation of Solution

Given:

The domain of $\left(f\cdot g\right)\left(x\right)$ consists of the numbers $x$ that are in the domains of both $f$ and $g$.

The domain of $\left(f\cdot g\right)\left(x\right)$ consists of the numbers $x$ that are in the domains of both $f$ and $g$. That is, domain of $f\cdot g=\text{ domain of }f\cap \text{domain of} g$.

Therefore the statement is false.