If `f(x)=x^(1//3)(x-2)^(2//3)` for all `x ,` then the domain of `f'` is `x in R-{0}` b. `{x|x>>0}` c. `x in R-{0,2}` d. `x in R`

If f(x)=x^(1//3)(x-2)^(2//3) for all x , then the domain of f' is a. x in R-{0} b. {x|x > 0} c. x in R-{0,2} d. x in R

If f(x)=x^(1//3)(x-2)^(2//3) for all x , then the domain of f' is a. x in R-{0} b. {x|x > 0} c. x in R-{0,2} d. x in R

Let 2f(x^(2))+3f(11x^(2))=x^(2)-1 for all x in R=[0], Then f(x) equals

Consider the function y=f(x) satisfying the condition f(x+(1)/(x))=x^(2)+1/x^(2)(x!=0) Then the domain of f(x) is R domain of f(x) is R-(-2,2) range of f(x) is [-2,oo] range of f(x) is (2,oo)

If 2f(x^(2))+3f((1)/(x^(2)))=x^(2)-1x varepsilon R_(0) then f(x^(2)) is

Let f(x+p)=1+{2-3f(x)+3(f(x))^2-(f(x)^3}^(1//3), for all x in R where p>0 , then prove f(x) is periodic.

If h(x)= f(f(x)) for all x in R, and f(x)= x^3 + 3x+2 , then h(0) equals

Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=(a) x for all x in R (b) x for all x in R-{1} (c) x for all x in R-{0,\ 1} (d) none of these

Assertion (A) : If f : R to R defined by f(x) =sin^(-1)(x/2) + log_(10)^(x) , then the domain of the function is (0,2]. Reason (R) : If D_(1) and D_2 are domains of f_(1) and f_2 , then the domain of f_(1) + f_(2) is D_(1) cap D_(2)

Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=x for all x in R (b) x for all x in R-{1} (c) x for all x in R-{0,\ 1} (d) none of these