Question:
Mark (√) against the correct answer in the following:
$f: R \rightarrow R: f(x)=\cos x$ is
A. one - one and into
B. one - one and onto
C. many - one and into
D. many - one and onto
Solution:
$f(x)=\cos x$
$y=\cos x$
Here in this range the lines cut the curve in many equal valued points of $y$ therefore the function $f(x)=$ cosx is not one - one.
$\Rightarrow f(x)=$ many one
Range of $f(x)=[-1,1] \neq R$ (codomain)
$\therefore f(x)$ is not onto.
$\Rightarrow f(x)=$ into
Hence, $f(x)=\cos x$ is many one and into
Ans: (c) many - one and into