Question

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

• A. If $f: R \rightarrow R$ and $g: R \rightarrow R$ 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 $g o f(x)$ must be periodic.

Answer 1

Answer: (A), (D)

Correct answer is (a) If $f: R \rightarrow R$ and $g: R \rightarrow R$ 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 $g o f(x)$ must be periodic.