Question 1205646
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Assuming {{{f(x) = log((x))-4}}} and not {{{f(x) = log((x-4))}}}, then {{{g(f(x)) = 1/(log((x)))}}} as shown by the other tutor.
It's ideal to be careful with parenthesis placement.


We cannot have x = 1 as an input since it leads to the denominator log(x) being zero.
log(1) = 0 for any valid base.


We also cannot have x = 0 nor negative x inputs since log(x) has the domain x > 0.
log(0) = undefined
log(anything negative) = undefined
I'll assume your teacher hasn't covered complex numbers quite yet. 



Answer: {{{x <= 0}}} or x = 1 lead to g(f(x)) being undefined.
Or you can expand things out a bit to say: x < 0 or x = 0 or x = 1 are three cases when g(f(x)) is undefined.
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