Question

Let $f_1:R\to R;f_2:[0,\infty )\to f_3:R\to R$ and $f_4:R\to [0,\infty )$ be defined by
$f_1\left(x\right)=|x|ifx<0=e^{x}ifx\ge 0f_2\left(x\right)=x^2{f}_3\left(x\right)=sinxifx<0=xifx\ge 0$
and $f_4\left(x\right)=f_2\left(f_1\right(x\left)\right),ifx<0f_2\left(f_1\right(x\left)\right)-1,ifx\ge 0$

$\begin{array}{cccc}& List-I& & List-II\\ P.& f_{2}is& 1.& \text{Onto but not one-one}\\ Q.& f_{3}is& 2.& \text{Neither continuous nor one-one}\\ R.& f_{4}is& 3.& \text{Differentiable but not one-one}\\ S.& f_{2}o{f}_{1}is& 4.& \text{Continuous and one-one}\end{array}$

• A. $\begin{array}{ccccc}& P& Q& R& S\\ \left(a\right)& 4& 3& 1& 2\end{array}$
• B. $\begin{array}{ccccc}& P& Q& R& S\\ \left(a\right)& 1& 3& 2& 4\end{array}$
• C. $\begin{array}{ccccc}& P& Q& R& S\\ \left(a\right)& 4& 3& 2& 1\end{array}$
• D. $\begin{array}{ccccc}& P& Q& R& S\\ \left(a\right)& 1& 3& 4& 2\end{array}$

Answer 1

The correct option is A

$\begin{array}{ccccc}& P& Q& R& S\\ \left(a\right)& 4& 3& 1& 2\end{array}$

$P:f_2:$

$Q:f_3:$

$R:f_4\left(x\right)=x^2,x<0=e^{2x-1},x\ge 0$

$S:$