Question

F(x) =

1
x
g(x) = x − 4
Can you evaluate (g ○ f)(0)? Explain why or why not.

Answer 1

No: heres the sample:

Explanation:

To evaluate the composition, you need to find the value of function f first. But, f(0) is 1 over 0, and division by 0 is undefined. Therefore, you cannot find the value of the composition.

have a good day :)

Answer 2

Explanation:

`f(x)=(1)/(x)\qquad\text{domain}:x\\eq0\\\\g(x)=x-4\qquad\text{domain}:x\in\mathbb{R}\\\\(g\circ f)(x)=g\bigg(f(x)\bigg)\Rightarrow (g\circ f)(x)=(1)/(x)-4\qquad\text{domain}:\ x\\eq0\\\\(g\circ f)(0)-\text{we can't calculate it because 0}\\.\qquad\qquad\text{ is not in the function domain.}\\\\\text{The expression}\ (1)/(0)\ \text{hasn't number sense}`