Question

$f:R\to R$ defined by $f(x)=\cos (2x+3)$ is

• A. injective only
• B. surjective only
• C. bijective
• D. neither injective nor surjective

Answer 1

Answer: (D)

$\cos (2x_1+3)=\cos (2x_2+3)\Rightarrow x_1\ne x_2\Rightarrow$ is not one-one .
Range of f = = [-1,1] $\ne$ codomain $\Rightarrow$ f is not onto