Question

I: The product of two odd functions is an even function.
II: A constant function is always a bijection.

• A. only I is true
• B. only II is true
• C. both I and II are true
• D. neither I nor II true

Answer 1

Answer: (A)

only I is true

I) Let $f$ and $g$ be two odd functions
Let $h\left(x\right)=f\left(x\right).g\left(x\right)$
$h(-x)=f(-x)g(-x)=(-f(x\left)\right)(-g(x\left)\right)$
$=f\left(x\right)g\left(x\right)$
$=h\left(x\right)$
$\therefore$ $h$ is an even function
$\therefore$ product of two odd functions is an even function.
II) A constant function is not a bjective function until its domain is also a single element:
i.e constant function is bijective iff its domain is singleton set.