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STD 12 - 1. relation and function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 1. relation and function4 Marks
MCQ
Greatest value of the function, $f(x) =  - 1 + \frac{2}{{{2^x}^2 + 1}}$ is 
  • A
    $1$
  • B
    $3/2$
  • C
    $2/3$
  • ✓
    $0$
✓

Answer

Correct option: D.
$0$
d
$f(x)=-1+\frac{2}{2^{x^{2}}+1}$

Clearly $f(x)$ in an even function and $f(x)$ is greatest

when $\frac{2}{2^{x^{2}}+1}$ is greatest.

(given)

Also, $\frac{2}{2^{x^{2}}+1}$ is greatest when $2^{x^{2}}+1$ is least,

which occurs when $x=0.$

Hence greatest value is $f(0)=0.$

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