SOLUTION: If f(x) = log x - 4 and g(x) = {{{1/(x+4)}}}, for what value(s) of x is g(f(x)) undefined? Explain by making reference to the algebraic properties (do not graph).

Question 1205646: If f(x) = log x - 4 and g(x) = , for what value(s) of x is g(f(x)) undefined? Explain by making reference to the algebraic properties (do not graph).
Found 2 solutions by MathLover1, math_tutor2020:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

for what value(s) of is undefined?
for is undefined, and it will be if

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Assuming and not , then 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: 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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