Question

Which of the following statement(s) is(are) CORRECT?

• A. If $f:R\to R$ and $g:R\to R$ be function such that $g(x)$ is onto and fog $(x)$ is injective then $g$ must be injective.
• B. Every function can be expressed as sum of two functions one of which is even and other is odd.
• C. If $f(x)$ and $g(x)$ are inverse of each other then $f\circ g(x)=g\circ f(x)$.
• D. If $f(x)$ is periodic and $g(x)$ is aperiodic then $gof(x)$ must be periodic.

Answer 1

Answer: (A), (D)

Correct answer is (a) If $f:R\to R$ and $g:R\to R$ be function such that $g(x)$ is onto and fog $(x)$ is injective then $g$ must be injective. Correct answer is (d) If $f(x)$ is periodic and $g(x)$ is aperiodic then $gof(x)$ must be periodic.