Home
Class 12
MATHS
Let f(1) : R to R, f(2) : [0, oo) to R, ...

Let `f_(1) : R to R, f_(2) : [0, oo) to R, f_(3) : R to R` be three function defined as
`f_(1)(x) = {(|x|, x < 0),(e^x , x ge 0):}, f_(2)(x)=x^2, f_(3)(x) = {(f_(2)(f_1(x)),x < 0),(f_(2)(f_1(x))-1, x ge 0):}` then `f_3(x)` is:

A

even function

B

odd function

C

neither even nor odd

D

periodic function

Text Solution

Verified by Experts

The correct Answer is:
C
`f_(3)(x) = {(f_2(|x|),x < 0),(f_2(e^x)-1,x ge0):}={(x^2 , x < 0),(e^(2x) - 1, x > 0):}`
Promotional Banner

Similar Questions

Explore conceptually related problems

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

The function f:R rarr R defined as f(x) = x^3 is:

the function f:R rarr R defined as f(x)=x^(3) is

Let f:R to R be a function defined b f(x)=cos(5x+2). Then,f is

Let f:R to R be the function defined by f(x)=2x-3, AA x in R. Write f^(-1).

Let f:R rarr R be the function defined by f(x)=x^(3)+5 then f^(-1)(x) is

Let f:R rarr R be a function defined as f(x)=(x^(2)-6)/(x^(2)+2) , then f is

Let f_(1):R rarr R,f_(2):[0,oo)rarr R,f_(3):R rarr R and f_(4):R rarr[0,oo) be defined by

Let f:R to R be a function defined by f(x)=(x^(2)-8)/(x^(2)+2) . Then f is

Let the function f: R to R be defined by f(x)=x^(3)-x^(2)+(x-1) sin x and "let" g: R to R be an arbitrary function Let f g: R to R be the function defined by (fg)(x)=f(x)g(x) . Then which of the folloiwng statements is/are TRUE ?