Question

Let f : R $\to$ R be any function. Define g : R $\to$ R by g(x) = |f(x)| for all x. Then g is

• A. onto if f is onto
• B. one-one if f is one-one
• C. continuous if f is continuous
• D. differentiable if f is differentiable

Answer 1

Answer: (C)

continuous if f is continuous

Answer 2

It is clear that the modulus function is continuous throughout the entire number line from its property.
Therefore, if f(x) is a continuous function, then the function described by g(x)=f(x) is continuous as well.

So, the correct answer is (C) continuous if f is continuous