Find the value of `x` where `f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot`

Column I: Function, Column II: Type of function f(x)="{"sgnx")"^(sgn)}; x!=0,n is an odd integer, p. odd function f(x)=x/(e^x-1)+x/2+1 , q. even function f(x)={0,ifxi sr a t ion a l1,ifxi si r r a t ion a l , r. neither odd nor even function. f(x)=max{tanx ,cotx} , s. periodic

Discuss the continuity of the following function : f(x)={1,ifxi sr a t ion a l0,ifxi si r r a t ion a l

"I f"f(x)={x^3-6x^2; ifxi sr a t ion a l-11 x+6;ifxi si r r a t ion a l"t h e n" f(x) is continuous for all real x f(x) is continuous at x=1,2,3. f(x) is discontinuous at infinite points f(x) discontinuous for all real xdot

If f(x)={x ,xi sr a t ion a l1-x ,xi si r r a t ion a l ,t h e nf(f(x)) is xAAx in R (b) {x , xi si r r a t ion a l1-x ,xi sr a t ion a l {x ,xi sr a t ion a l1-x ,xi si r r a t ion a l (d) none of these

If the functions f(x)a n dg(x) are defined on R rarr R such that f(x)={0, x in r a t ion a l x ,x in i r r a t ion a l a n dg(x)={O , x in i r r a t ion a l x ,x in r a t ion a l then (f-g)(x)i s (a)one-one and onto (b)neither one-one nor onto (c)one-one but not onto (d)onto but not one-one

Let f(x)={2/(1+x^2),xi sr a t ion a l b ,xi sr a t ion a l has exactly two points of continuity then the value of b are (0,3] b. [0,1] c. (0,2] d. varphi

Find the value of f(0) so that the function. f(x)=(sqrt(1+x)-1+x3)/xb e com e scon t inuou sa tx=0

Find the derivative of x^(2) sinx w.r.t.x.

Find the derivative of sin x^(@) w.r.t. x

Find the derivative of x^x-2^(sinx) w.r.t. x