Question

f(x) = 1/x, g(x) = |x| - 2
What is the domain of (f*g)(x)?
{x|x E real numbers}
{x|x ≠ 0}
{x|x ≠ -2, x ≠ 2}
{x|x ≠ 0, x ≠ 2}

Answer 1

f(g(x)) = f(|x| - 2) = 1 / |x| - 2

The denominator should not be equal to zero, because then it would become undefined.
Equate the denominator to zero.
|x| - 2 = 0
Since x is in absolute value,
When x is +: x - 2 = 0; x =2
When x is -: -x - 2 = 0; x = -2

So the x should not be equal to 2 and -2.

Answer 2

So the domain is {x|x ≠ -2, x ≠ 2}. Thanks1