Question

f(x) = 1/x
g(x) = x - 4
Can you evaluate (gof)(0)? Explain why or why
not.

Answer 1

(gof)(0) cannot be evaluated

Solution:

Given that,

$f(x) = \frac{1}{x}\\\\g(x) = x - 4$

A composite function is denoted by (g o f) (x) = g (f(x)).

The notation g o f is read as “g of f”

Therefore, let us find whether (gof)(0) can be evaluated or not

To find (gof)(0):

(g o f) (x) = g (f(x))

Now substitute the given value of f(x)

$(g o f) (x) = g(\frac{1}{x})$

$\text{ Substitute } x = \frac{1}{x} \text{ in } g(x) = x - 4$

$(g o f) (x) = \frac{1}{x} - 4$

Now to find (gof)(0), substitute x = 0

$(g o f) (x) = \frac{1}{0} - 4$

Since 1 divided by 0 is undefined, because any number divided by 0 is undefined

(gof)(0) cannot be evaluated

Answer 2

Answer:

You must evaluate the function f first.

Division by 0 is undefined.

The composition cannot be evaluated.

Step-by-step explanation: