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`

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

If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x) , then the value of g'(1) is

The value of parameter alpha , for which the function f(x) = 1+alpha x, alpha!=0 is the inverse of itself

Let f(x)=(alphax)/(x+1),x ne -1 . Then, for what values of alpha is f[f(x)]=x?

If alpha=2 tan^(-1)((1+x)/(1-x)) and beta= sin^(-1)((1-x^2)/(1+x^2)) for 0 lt x lt 1 ,then prove that alpha+beta =pi , what the value of alpha+beta will be if x gt 1 .

If a_(1),a_(2),".....", are in HP and f_(k)=sum_(r=1)^(n)a_(r)-a_(k) , then 2^(alpha_(1)),2^(alpha_(2)),2^(alpha_(3))2^(alpha_(4)),"....." are in {" where " alpha_(1)=(a_(1))/(f_(1)),alpha_(2)=(a_(2))/(f_(2)),alpha_(3)=(a_(3))/(f_(3)),"....."} .

If alpha is a root of the equation 4x^2+2x-1=0, then prove that 4alpha^3-3alpha is the other root.

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

Let f(x)=x^(2)+bx+c and g(x)=x^(2)+b_(1)x+c_(1) Let the real roots of f(x)=0 be alpha, beta and real roots of g(x)=0 be alpha +k, beta+k fro same constant k . The least value fo f(x) is -1/4 and least value of g(x) occurs at x=7/2 The roots of g(x)=0 are

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