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

1.	Let f1:R→R;f2:[0,∞)→f3:R→R and f4:R→[0,∞) be defined by f1(x)=\|x\| if x<0=exifx≥0f2(x)=x2f3(x)=sin x if x<0=x ifx≥0 and f4(x)=f2(f1(x)), ifx<0f2(f1(x))−1, ifx≥0 List−IList−IIP.f2 is1.Onto but not one-oneQ.f3 is2.Neither continuous nor one-oneR.f4 is3.Differentiable but not one-oneS.f2 of1is4.Continuous and one-one
Answer» 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 $f_{1} (x) = \| x \| i f x < 0 = e^{x} i f x \geq 0 f_{2} (x) = x^{2} f_{3} (x) = s i n x i f x < 0 = x i f x \geq 0$ and $f_{4} (x) = f_{2} (f_{1} (x)), i f x < 0 f_{2} (f_{1} (x)) - 1, i f x \geq 0$ $\begin{matrix} L i s t - I & L i s t - I I P . & f_{2} i s & 1. & Onto but not one-one Q . & f_{3} i s & 2. & Neither continuous nor one-one R . & f_{4} i s & 3. & Differentiable but not one-one S . & f_{2} o f_{1} i s & 4. & Continuous and one-one \end{matrix}$

Let f1:R→R;f2:[0,∞)→f3:R→R and f4:R→[0,∞) be defined by f1(x)=|x| if x<0=exifx≥0f2(x)=x2f3(x)=sin x if x<0=x ifx≥0 and f4(x)=f2(f1(x)), ifx<0f2(f1(x))−1, ifx≥0 List−IList−IIP.f2 is1.Onto but not one-oneQ.f3 is2.Neither continuous nor one-oneR.f4 is3.Differentiable but not one-oneS.f2 of1is4.Continuous and one-one

Answer»

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
$f_{1} (x) = | x | i f x < 0 = e^{x} i f x \geq 0 f_{2} (x) = x^{2} f_{3} (x) = s i n x i f x < 0 = x i f x \geq 0$
and $f_{4} (x) = f_{2} (f_{1} (x)), i f x < 0 f_{2} (f_{1} (x)) - 1, i f x \geq 0$

$\begin{matrix} L i s t - I & L i s t - I I P . & f_{2} i s & 1. & Onto but not one-one Q . & f_{3} i s & 2. & Neither continuous nor one-one R . & f_{4} i s & 3. & Differentiable but not one-one S . & f_{2} o f_{1} i s & 4. & Continuous and one-one \end{matrix}$

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