Given $f(x)=\cos x ,\forall x,\in R$
Let $f(x)=f(y)=1$
Step1: Injective or One-One function:
but $0 \neq 2\pi$
Hence f is not a one-one function
Step 2: Surjective or On-to function:
Consider $y=2 \in R$
There does not exist any $x \in R$ such that $f(x)=\cos x=y=2$
$\cos x$ can take values from -1 to 1 only
Hence f is not a onto function
$\textbf{Solution: Therefore f is neither one-one nor onto}$