Question

is the statement |f(x)|= f|(|x)| always true, sometimes true or never true use examples.

If f(x) means the function of x then it means the absolute value of the function of x equals the function of the absolute value of x. I do not know how to provide examples but I believe this is true because if you take the absolute value of |f(x)| is it not the same as the function of absolute value of x

Answer 1

let f(x)=3 for all x

then abs(f(x)) is true
but let f(x)=3 for all x>0, and =-3 for all x<0
then f(abs(x))does not equal abs(f(x))

so, I rate the statement sometimes true.