Question

Let f: R → R be any function. Define g : R → R by g(x)

= |f(x)| for all x. Then g is (2000 S)

• 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

Let h (x) = |x| then g(x) |f(x)| = h)(f(x))

Since composition of two continuous function is continuous, g is continuous if f is continuous.