Let f1:R→R, f2:[0,∞)→R, f3:R→R and f4:R→[0,∞) be defined byf1(x)={|x| if x<0, ex if x≥0;f2(x)=x2;f3(x)={sinx if x<0, x if x≥0;andf4(x)={f2(f1(x)) if x<0,f2(f1(x))−1 if x≥0.List IList IIP. f4 is 1. onto but not one-oneQ. f3 is 2. neither continuous nor one-one R. f2∘f1 is 3. differentiable but not one-oneS. f2 is 4. continuous and not one-onewhich of the following option is correct ?

Let f1:R→R, f2:[0,∞)→R, f3:R→R and f4:R→[0,∞) be defined b

1.	Let f1:R→R, f2:[0,∞)→R, f3:R→R and f4:R→[0,∞) be defined byf1(x)={\|x\| if x<0, ex if x≥0;f2(x)=x2;f3(x)={sinx if x<0, x if x≥0;andf4(x)={f2(f1(x)) if x<0,f2(f1(x))−1 if x≥0.List IList IIP. f4 is 1. onto but not one-oneQ. f3 is 2. neither continuous nor one-one R. f2∘f1 is 3. differentiable but not one-oneS. f2 is 4. continuous and not one-onewhich of the following option is correct ?
Answer» Let $f_{1} : R \to R,$ $f_{2} : [0, \infty) \to R,$ $f_{3} : R \to R$ and $f_{4} : R \to [0, \infty)$ be defined by $f_{1} (x) = {\begin{matrix} \| x \| if x < 0, e^{x} if x \geq 0; \end{matrix}$ $f_{2} (x) = x^{2};$ $f_{3} (x) = {\begin{matrix} sin x if x < 0, x if x \geq 0; \end{matrix}$ and $f_{4} (x) = {\begin{matrix} f_{2} (f_{1} (x)) if x < 0, f_{2} (f_{1} (x)) - 1 if x \geq 0. \end{matrix}$ $\begin{matrix} L i s t I & L i s t I I P. f_{4} is & 1. onto but not one-one Q. f_{3} is & 2. neither continuous nor one-one R. f_{2} \circ f_{1} is & 3. differentiable but not one-one S. f_{2} is & 4. continuous and not one-one \end{matrix}$ which of the following option is correct ?