Statement – I :  Every strictly monotonic function is one one.

Statement – II : The function $f:R^{+}\to Rdefinedbyf\left(x\right)=5+x^2$ is one one.

Which of the following is true

Statement – I : Strictly monotonic function is one - one.  Statement 1 is true.

Statement – II :

$\begin{array}{l}f\left(x\right)=5+x^{2}andf:R^{+}\to R\\ Let{x}_1,x_2\in R^{+}\\ \therefore f\left(x_1\right)=f\left(x_2\right)\Rightarrow 5+x_1^2=5+x_2^2\\ \Rightarrow x_1^2=x_2^2\\ \Rightarrow x_1=x_2\left(\because x_1,x_2\in R^{+}\right)\\ \therefore f\left(x\right)isone-one\\ Statement-IIistrue\end{array}$