Use the given functions to find g(f(x)), and give the restrictions on x.

Question

f(x)=1/x-4
g(x)=(3/x)+4

I'm having trouble find the restrictions for x

Answer 1

I assume you made a parenthesis mistake and mean
1 / (x-4)

g( f(x) )=(3/{ 1/(x -4) } )+4
g( f(x) )=(3( x-4) )+4
= 3 x - 12 + 4
= 3 x - 8

Answer 2

I got that part correct. Thank you!
But how do I look for the restrictions on x?

So where x=/= ?

Answer 3

When x = 4 you have a zero denominator

Then you have
g( f(x) )=(3/{ 1/ (ZERO) } )+4

Answer 4

So restrictions would be 4 and 0?

I don't know why this is confusing me so much!!!

Answer 5

Just 4
because x=4 gives 4-4 = 0 in the denominator