Given `g(x)=(x+2)/(x-1)` and the line `3x+y-10=0.` Then the line is tangent to `g(x)` (b) normal to `g(x)` chord of `g(x)` (d) none of these

Let g(x)=2f(x/2)+f(x) and f''(x)lt0 " in "0lexle1 , then g(x)

Let f(x)=(1)/(1+x^(2)) and g(x) is the inverse of f(x) ,then find g(x)

If f(x)=x+tanx and g(x) is the inverse of f(x), then differentiation of g(x) is (a) 1/(1+[g(x)-x]^2) (b) 1/(2-[g(x)+x]^2) (c) 1/(2+[g(x)-x]^2) (d) none of these

Given that f'(x) > g'(x) for all real x, and f(0)=g(0) . Then f(x) < g(x) for all x belong to (a) (0,oo) (b) (-oo,0) (c) (-oo,oo) (d) none of these

If g is the inverse function of fa n df^(prime)(x)=sinx ,t h e ng^(prime)(x) is (a) cos e c{g(x)} (b) "sin"{g(x)} (c) -1/("sin"{g(x)}) (d) none of these

Let g(x) be the inverse of f(x) and f'(x)=1/(1+x^3) . Then find g'(x) in terms of g(x).

If g(x)=int_0^x(|sint|+|cost|)dt ,then g(x+(pin)/2) is equal to, where n in N , (a) g(x)+g(pi) (b) g(x)+g((npi)/(2)) (c) g(x)+g(pi/2) (d) none of these

If f(x)=kx^(2)-3x+k and g(x) = x - 1 be two polynomials, then g(x) will be a factor of f(x) when k =

If f(a)=2,f^(prime)(a)=1,g(a)=-1,g^(prime)(a)=2, then the value of lim_(x->a)(g(x)f(a)-g(a)f(x))/(x-a) is (a) -5 (b) 1/5 (c) 5 (d) none of these

If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that f(0)=10 ,g(0)=2,f(1)=2,g(1)=4, then in the interval (0,1)dot (a) f^(prime)(x)=0 for a l lx (b) f^(prime)(x)+4g^(prime)(x)=0 for at least one x (c) f(x)=2g'(x) for at most one x (d) none of these