If `f: R->R ,f(x)=(alphax^2+6x-8)/(alpha+6x-8x^2)` is onto then `alpha in`

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=1)^(20)a_k x^k , then prove that the value of f(x)+f(alpha, x)++f(alpha^6x) is independent of alphadot

For function f(x) = (alpha x)/(x+1) , x ne -1 if fof(x) = x then alpha = ..........

Show that f: R rarr R , f(x) = x/(x^(2)+1) is not one one and onto function.

f: R rarr R, f(x) = sec^(2)x - tan^(2) x is constant function .

Let alpha, beta in R such that lim_(x ->0) (x^2sin(betax))/(alphax-sinx)=1 . Then 6(alpha + beta) equals

If f:R rarr [pi/6,pi/2], f(x)=sin^(-1)((x^(2)-a)/(x^(2)+1)) is an onto function, the set of values a is

If f(x) is a polynomial of degree n(gt2) and f(x)=f(alpha-x) , (where alpha is a fixed real number ), then the degree of f'(x) is

Let f(x) is a polynomial function and f(alpha))^(2) + f'(alpha))^(2) = 0 , then find lim_(x rarr alpha) (f(x))/(f'(x))[(f'(x))/(f(x))] , where [.] denotes greatest integer function, is........

f: R rarr R , f(x) = (x-1) (x-2)(x-3) then f is ........

If f: R -> R and g: R ->R are two given functions, then prove that 2min {f(x)-g(x),0}=f(x)-g(x)-|g(x)-f(x)|