Question

What is the domain of (f/g)(x) if f(x)=x g(x)=1

Answer 1

Answer:

Domain: (-∞,∞) OR All Real Numbers

Step-by-step explanation:

(f/g)(x) ⇒ f(x)/g(x) ⇒ x/1

Therefore, we look at the domain of the function x/1. There will almost always only be a gap if the denominator = 0. However, 1 ≠ 0, so therefore, there are no gaps or endpoints. Therefore, the domain is all real numbers

Answer 2

The domain of a function is the set of all the values of the variable (x) for which the function has a possible output.

The domain of the composite function $f(g(x))$ is all the real number from negative infinity to positive infinity.

Given information-

The function given in the problem is,

$f(x)=x$

$g(x)=1$

What is domain?

The domain of a function is the set of all the values of the variable (x) for which the function has a possible output.

The domain of $f(g(x))$ find out in two parts as-

• Domain when $f(g(x))$ is a function
• Domain of the function $g(x)$

As the function $f(x)$ has the variable x. Put the value of $g(x)$ (which is one) in this function to get,

$f(g(x))=\dfrac{x}{1}$

Hence the domain of $f(g(x))$ is all real numbers as one can not be equal to zero.

The domain of interior function is,

$g(x)=1$

Hence the domain of $(g(x))$ is  1.

Thus the domain of the composite function $f(g(x))$ is all the real number from negative infinity to positive infinity.

Learn more about the domain of the function here;

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