" (iti) "f(x)={[x^(2)sin(1)/(x)," if "x!=0,,],[0,," if "x,=0,,(N.C.E.R.T.)]

Let f:R rarr R be defined by f(x)={x+2x^(2)sin((1)/(x)) for x!=0,0 for x=0 then

Let f(x)={{:(x^(n)sin(1//x^(2))","xne0),(0", "x=0):},(ninI). Then

Let f_(1):R to R, f_(2):[0,oo) to R, f_(3):R to R and f_(4):R to [0,oo) be a defined by f_(1)(x)={{:(,|x|,"if "x lt 0),(,e^(x),"if "x gt 0):}:f_(2)(x)=x^(2),f_(3)(x)={{:(,sin x,"if x"lt 0),(,x,"if "x ge 0):} and f_(4)(x)={{:(,f_(2)(f_(1)(x)),"if "x lt 0),(,f_(2)(f_(1)(f_(1)(x)))-1,"if "x ge 0):} then f_(2) of f_(1) is

Let f_(1):R to R, f_(2):[0,oo) to R, f_(3):R to R and f_(4):R to [0,oo) be a defined by f_(1)(x)={{:(,|x|,"if "x lt 0),(,e^(x),"if "x gt 0):}:f_(2)(x)=x^(2),f_(3)(x)={{:(,sin x,"if x"lt 0),(,x,"if "x ge 0):} and f_(4)(x)={{:(,f_(2)(f_(1)(x)),"if "x lt 0),(,f_(2)(f_(1)(f_(1)(x)))-1,"if "x ge 0):} then f_(2) is

Consider the function f:R to R defined by f(x)={((2-sin((1)/(x)))|x|,",",x ne 0),(0,",",x=0):} .Then f is :

Let f(1):R to R, f_(2):[0,oo) to R, f_(3):R to R and f_(4):R to [0,oo) be a defined by f_(1)(x)={{:(,|x|,"if "x lt 0),(,e^(x),"if "x gt 0):}:f_(2)(x)=x^(2),f_(3)(x)={{:(,sin x,"if x"lt 0),(,x,"if "x ge 0):} and f_(4)(x)={{:(,f_(2)(f_(1)(x)),"if "x lt 0),(,f_(2)(f_(1)(f_(1)(x)))-1,"if "x ge 0):} Then, f_(4) is

Let f(1):R to R, f_(2):[0,oo) to R, f_(3):R to R and f_(4):R to [0,oo) be a defined by f_(1)(x)={{:(,|x|,"if "x lt 0),(,e^(x),"if "x gt 0):}:f_(2)(x)=x^(2),f_(3)(x)={{:(,sin x,"if x"lt 0),(,x,"if "x ge 0):} and f_(4)(x)={{:(,f_(2)(f_(1)(x)),"if "x lt 0),(,f_(2)(f_(1)(f_(1)(x)))-1,"if "x ge 0):} Then, f_(4) is

Deine F(x) as the product of two real functions f_1(x) = x, x in R, and f_2(x) ={ sin (1/x), if x !=0, 0 if x=0 follows : F(x) = { f_1(x).f_2(x) if x !=0, 0, if x = 0. Statement-1 : F(x) is continuous on R. Statement-2 : f_1(x) and f_2(x) are continuous on R.