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umka2103 [35]
3 years ago
14

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

Mathematics
2 answers:
s344n2d4d5 [400]3 years ago
6 0

(gof)(0) cannot be evaluated

<em><u>Solution:</u></em>

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

Lyrx [107]3 years ago
5 0

Answer:

You must evaluate the function f first.

Division by 0 is undefined.

The composition cannot be evaluated.

Step-by-step explanation:

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