A) \[[1,\,\,\infty )\]
B) \[[2,\,\,\infty )\]
C) \[\left[ \frac{3}{2},\,\,\infty \right)\]
D) None of these
Correct Answer: A
Solution :
Given,\[f(x)={{x}^{2}}+\frac{1}{{{x}^{2}}+1}\] \[\therefore \] \[f(x)={{x}^{2}}+\left( \frac{1}{{{x}^{2}}+1}-1 \right)+1\] \[=({{x}^{2}}+1)-\left( \frac{{{x}^{2}}}{{{x}^{2}}+1} \right)\] \[=1+{{x}^{2}}\left( 1-\frac{1}{{{x}^{2}}+1} \right)\] \[\ge 1,\,\forall x\in R\] Hence, range of\[f(x)\]is\[[1,\,\,\infty )\].
You need to login to perform this action.
You will be redirected in
3 sec
