The domain of f(x) is the set of all real values except 7, and the domain of g(x) is the set of all real values except -3 Which of the following describes the domain of (gcirc f)(x) all real values except xneq -3 and the x for which f(x)neq 7 all real values except xneq -3 and the x for which f(x)neq -3 all real values except xneq 7 and the x for which f(x)=7 all real values except xneq 7 and the x for which f(x)neq -3

Question

Pergunta

Answer 1

To find the domain of

$(g\circ f)(x)$ , we need to consider the domains of both

$f(x)$ and

$g(x)$ .

The domain of

$f(x)$ is the set of all real values except 7. This means that

$f(x)$ is defined for all real values of

$x$ except when

$x = 7$ .

The domain of

$g(x)$ is the set of all real values except

$-3$ . This means that

$g(x)$ is defined for all real values of

$x$ except when

$x = -3$ .

When we compose

$g$ with

$f$ , we need to ensure that the output of

$f(x)$ is within the domain of

$g(x)$ . In other words, we need to find the values of

$x$ for which

$f(x) \neq -3$ .

Therefore, the domain of

$(g\circ f)(x)$ is the set of all real values except

$x\neq 7$ and the

$x$ for which

$f(x)\neq -3$ .

So, the correct answer is: all real values except

$x\neq 7$ and the

$x$ for which

$f(x)\neq -3$ .