Answer:
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.
Step-by-step explanation:
NO, because the resulting function for (g ○ f)(0) tends to infinity
An undefined term or function is a term or function that does not exsit.
A composite function is a function that is placed in another function.
Given the functions
f(x) = 1/x g(x) = x − 4
Before we can calculate the composite function (g ○ f)(0), we ned to first calculate (g ○ f)(x) as shown:
(g ○ f)(x) = g(f(x))
g(f(x)) = g(1/x)
Substitute x as 1/x in g(x) as shown:
[tex]g(f(x)) =g(\frac{1}{x} )\\g(\frac{1}{x} )=(\frac{1}{x}-4 )\\Find \ the \ LCM\\g(\frac{1}{x} )=(\frac{1-4x}{x} )\\[/tex]
NExt is to check whether we can evaluate (g ○ f)(0) by substituting x = 0 into the resulting function as shown:
[tex]g(f(0) )=(\frac{1-4(0)}{0} )\\g(f(0) )=(\frac{1}{0} )\\g(f(0) )=\infty[/tex]
We can see that the resulting function tends to infinity which shows that g ○ f)(0) cannot be evaluated.
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