A) one-one but not onto
B) one-one and onto
C) onto but not one-one
D) neither one-one nor onto
Correct Answer: D
Solution :
We have, \[f(x)=\frac{{{x}^{2}}-8}{{{x}^{2}}+2}\] Clearly, \[f(-x)=f(x)\]. Therefore, \[f\] is not one-one. Again, \[f(x)=\frac{{{x}^{2}}-8}{{{x}^{2}}+2}=1-\frac{10}{{{x}^{2}}+2}\] \[\Rightarrow \] \[f(x)<1\]for all \[x\in R\] \[\Rightarrow \]Range of f \[\ne \]codomain of f, i.e.R So, f is not onto. Hence, f is neither one-one nor onto.
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