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).

Algebra ->  Functions -> 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).      Log On


   

Question 1205646: If f(x) = log x - 4 and g(x) = 1%2F%28x%2B4%29, 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) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29+=+log+%28x%29+-+4+
g%28x%29+=+1%2F%28x%2B4%29
g%28f%28x%29%29+=g%28log+%28x%29+-+4%29+=1%2F%28log+%28x%29+-+4%2B4%29=1%2Flog+%28x%29

for what value(s) of x is g%28f%28x%29%29 undefined?
for log+%28x%29=0 g%28f%28x%29%29 is undefined, and it will be if x=1

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

Assuming f%28x%29+=+log%28%28x%29%29-4 and not f%28x%29+=+log%28%28x-4%29%29, then g%28f%28x%29%29+=+1%2F%28log%28%28x%29%29%29 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+%3C=+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.