If `f(n)=alpha^n+beta^n` then show that
`|{:(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f(3)),(1+f(2),1+f(3),1+f(4)):}|=(1-alpha)^2(1-beta)^2(alpha-beta)^2`

If alpha,beta!=0 ,and f(n)""=alpha^n+beta^n and |{:(3,1+f(1),1+f(2)),(1+f(1),1+f(2),1+f(3)),(1+f(2),1+f(3),1+f(4)):}| =K (1-alpha)^2(1-beta)^2(alpha-beta)^2 ,then K is equal to

If f(x)= x^(3)- (1)/(x^(3)) then show that f(x)+ f((1)/(x))= 0

If f(x)= (x-1)/(x+1) , Then show that f(-(1)/(x))= (-1)/(f(x))

If f(x)= x^(2 )+ 2x + 3 then find f(1), f(2), f(3)

If f(x)=x^(2)," find "(f(1.1)-f(1))/((1.1-1))

f:R rarr R , f(x) = {(12x+5,x gt1),(x-4,xle1):} then find f(0),f(-1/2), f(3),f(-5) .

If 2f (x)- 3f((1)/(x))= x^(2) (x ne 0) then f(2)= ……

If f'(x)=x-(1)/(x^(2)) and f(1)=(1)/(2) then find f(x).

If alpha and beta are the roots of the equation x^2-4x + 1=0(alpha > beta) then find the value of f(alpha,beta)=(beta^3)/2csc^2(1/2tan^(- 1)(beta/alpha))+(alpha^3)/2sec^2(1/2tan^- 1(alpha/beta))

Statement -1 If Delta(r)=|{:(r,r+1),(r+3,r+4):}| then sum_(r=1)^(n) Delta(r)=-3n Satement-2 If Delta(r)=|{:(f_(1)(r),f_(2)(r)),(f_(3)(r),f_(4)(r)):}| Sigma_(r=1)^(n) Delta (r)={:abs((Sigma_(r=1)^(n)f_1(r),Sigma_(r=1)^(n)f_2(r)),(Sigma_(r=1)^(n)f_3(r),Sigma_(r=1)^(n) f_4(r))):}