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1. relation and function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths1. relation and function1 Mark
MCQ
$f : R \rightarrow  (-1,1), f(x) = \frac{e^x - 1}{e^x + 1}$ is
  • A
    one-one into
  • ✓
    one-one onto
  • C
    many one into
  • D
    many-one onto
✓

Answer

Correct option: B.
one-one onto
b
$f(x)=1-\frac{2}{e^{x}+1}$

range of $f(x)=(-1,1)$

$f^{\prime}(x)=+\frac{2 e^{x}}{\left(e^{x}+1\right)^{2}}>0 \forall x \in R$

so $f(x)$ is one-one onto

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