Question

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

Answer 1

(g of)(0) = 1/0-4

Explanation:

We have given two functions.

f(x) = 1/x and g(x) = x-4

We have to calculate (g of)(0).

The formula to calculate (g o f)(x) is :

(g of)(x) = g(f(x))

Putting values in above formula, we have

(g of)(x) = g(1/x)

(g of)(x) = 1/x-4

(g of)(0) = 1/0-4

Since , we know that 1/0 does not exist.

We can't evaluate (g of)(0).

Answer 2

No

Explanation:

We have the following two functions:

`f(x) = (1)/(x)`

`g(x) = x-4`

The product of the two functions can be calculated as:

`(g \cdot g)(f) = (x-4) \cdot ((1)/(x)) = (x-4)/(x)`

We see that the domain of this new function is all real numbers, except from zero, which is excluded. Therefore, it is not possible to evaluate the function at x=0, so it is not possible to calculate (g ○ f)(0).