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

A function f : R rarr R, where R is the set of real numbers, is defined by : f(x)= (alpha x^2+6x-8)/(alpha+6x-8x^2) . Find the interval of values of alpha for which f is onto. Is the function one-one for alpha = 3 ? Justify your answer.

If alpha=e^(i2pi//7)a n df(x)=a_0+sum_(k=0)^(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(x) = alpha x^n , prove that alpha= (f'(1))/n .

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)=(x^(2)+2alphax+alpha^(2)-1)^(1//4) has its domain and range such that their union is set of real numbers, then alpha satisfies

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........

If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is one-one, we need to differentiate f(x). If f'(x) changes sign in domain of f, then f, if many-one else one-one. If f:R rarr R and f(x)=2ax +sin2x, then the set of values of a for which f(x) is one-one and onto is

Let A = R- {3} and B = R- {1}. If f: ArarrB is a function defined by f(x)= (x-2)/(x-3) show that f is one -one and onto, hence find f^(-1) .