Question

please help out!! it is urgent.

Answer 1

hi there!!

Let h(x) = |x|,
 then, g(x) = |f (x)|= h{ f(x) }
Since, composition of two continuous functions is continuous, g is continuous. So,answer is (c).

In case of (a), 
Let f(x) = x => g(x) = |x|
Now, f(x) is an onto function. Since, co-domain is given R.
Hence (a) option is wrong.

In case of (b),
Let f(x) = x => g(x) = |x|. 
Now, f(x) is one-one function but g(x) is many-one function.
Hence, (b) option is wrong.

In case of (d),
Let f(x) = x => g(x) = |x|.
Now, f(x) is differentiable for all x∈R but g(x) = |x| is not differentiable at x=0.
Hence, (d) option is also wrong.

HOPE YOU GET YOUR ANSWER!!!
# RUHANIKA