Answered

Let f(x) = x – 4 and g(x)=1/x. The graph of (g o f)(x) is shown below.

What is the domain of (g o f)(x)?


all real numbers except x = –4

all real numbers except x = 0

all real numbers except x = 4

all real numbers

Verified Answer :

Dontthankmebrainme

Oi-All real numbers except x=4 

they would all intersect 0 still

Answer:

domain is all real numbers except x=4

Step-by-step explanation:

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

We need to find (gof)(x)

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

Plug in x-4 for f(x)

\((g o f)(x)= g(f(x))=g(x-4)\)

Now we plug in x-4 for x in g(x)

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

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

Domain is the set of all x values for which the function is defined

To find out the x values that is undefined we set the denominator =0 and solve for x

\(x-4=0, x=4\)

When x=4 the denominator becoems 0 that is undefined

So domain is all real numbers except x=4

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