Greatest value of the function, f(x) = - 1 + 2 2^x ^2 + 1 is - Vidyadip

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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