Let `f(x)=x^3-6x^2+3(1+pi)x+7, pgtqgtr, then ({x-f(p)}(x-f(r)}}/(x-f(q))` has no value in (A) (p,q) (B) (q,r) (C) `(r,oo)` (D) none of these

Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x) is invertible if (a)a in (-5,5) (b) a in (-oo,5) (c)a in (-5,+oo) (d) none of these

Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3) (b) sqrt(x)+3 (c) x+sqrt(3) (d) none of these

f(x) = (x (x-p))/(q - p) + (x (x - q))/(p - q) , p ne q. What is the value of f (p) + f(q) ?

If range of the function f(x)=(2sin^(2)x+2sin x+3)/(sin^(2)x+sin x+1)is[p,q], then the value of 3p+6q+1 is (10)/(3) (b) (7)/(3)(c)28 (d) None of these

Let a,b,c be the roots of the equation x^(4)+x^(3)+x^(2)+x-1=0. Let f(x)=x^(6)-6x^(2)+6x+7 and g(x)=px^(2)+qx+r , (p,q,r in R,p!=0). If f(a)=g(a); f(b)=g(b) and f(c)=g(c); then the value of (2)/(g(1)) is

Let f(x)=x^(3)-6x^(2)+15x+3. Then,(a) f(x)>0 for all x in R( b) f(x)>f(x+1) for all x in R( cl )f(x) is invertible (d) f(x)<0 for all x in R

let f(x)=5 , -oo 1) f(g(x))=5 then find the value of 2p+q

Let f(x)=(2x-pi)^(3)+2x-cos x .If the value of (d)/(dx)(f^(-1) (x)) at x=pi can be expressed in the form of (p)/(q) ( where p and q are natural numbers in their lowest form), then the value of (p+q) is

If f(x)=sqrt(x^(2)+6x+9), then f'(x) is equal to 1 for x<-3( b) -1 for x<-3(c)1 for all x in R(d) none of these