the domain of $u(x)$ is the set of all real values except 0 and the domain of $v(x)$ is the set of all real…

the domain of $u(x)$ is the set of all real values except 0 and the domain of $v(x)$ is the set of all real values except 2. what are the restrictions on the domain of $(ucirc v)(x)$?\n$u(x)\neq0$ and $v(x)\neq2$\n$x\neq0$ and $x$ cannot be any value for which $u(x) = 2$\n$x\neq2$ and $x$ cannot be any value for which $v(x)=0$\n$u(x)\neq2$ and $v(x)\neq0$

the domain of $u(x)$ is the set of all real values except 0 and the domain of $v(x)$ is the set of all real values except 2. what are the restrictions on the domain of $(ucirc v)(x)$?\n$u(x)\neq0$ and $v(x)\neq2$\n$x\neq0$ and $x$ cannot be any value for which $u(x) = 2$\n$x\neq2$ and $x$ cannot be any value for which $v(x)=0$\n$u(x)\neq2$ and $v(x)\neq0$

Answer

Explanation:

Step1: Recall definition of composition

The composition ((u\circ v)(x)=u(v(x))). For (u(v(x))) to be well - defined, (v(x)) must be in the domain of (u(x)).

Step2: Consider domain of (u(x))

The domain of (u(x)) is all real values except (0). So (v(x)\neq0).

Step3: Consider domain of (v(x))

The domain of (v(x)) is all real values except (2). So (x\neq2).

Answer:

C. (x\neq2) and (x) cannot be any value for which (v(x) = 0)