In which of the function is one-one- - Vidyadip

MCQ

In which of the function is one-one-

A
$f: R \rightarrow R$,$
f(x)=x^2
$
✓
$f: R \rightarrow R$,$
f(x)=x+1
$
C
$f: R \rightarrow R$,$
f(x)=e^x+e^{-x}
$
D
$f: R \rightarrow R$,$
f(x)=3 x^2
$

✓

Answer

Correct option: B.

$f: R \rightarrow R$,$
f(x)=x+1
$

(B) $f: R \rightarrow R , \quad f(x)=x+1$
Suppose $x_1, x_2 \in R$ such that
$\begin{aligned} & & f\left(x_1\right) & =f\left(x_2\right) \\ \Rightarrow & & x_1+1 & =1 \\ \Rightarrow & & x_1 & =x_2+1\end{aligned}$
hence $f\left(x_1\right)=f\left(x_2\right) \Rightarrow x_1=x_2 \forall x_1, x_2 \in R$
$\therefore f$ is one-one function.

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