Question

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

Answer 1

Oi-All real numbers except x=4

they would all intersect 0 still

Answer 2

domain is all real numbers except x=4

Explanation:

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

`(g o f)(x)=(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