Suppose `f(x)=a x+ba n dg(x)=b x+a ,w h e r eaa n db` are positive integers. If `f(g(20))-g(f(20))=28 ,` then which of the following is not true? `a=15` b. `a=6` c. `b=14` d. `b=3`

If f(x)=x/(sinx)a n dg(x)=x/(tanx),w h e r e0ltxlt=1, then in this interval

If f(x)=a x^2+b x+c ,g(x)=-a x^2+b x+c ,w h e r ea c!=0, then prove that f(x)g(x)=0 has at least two real roots.

if f(x) =ax +b and g(x) = cx +d , then f[g(x) ] - g[f(x) ] is equivalent to

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot

If f(x)a n dg(x) are two positive and increasing functions, then which of the following is not always true? [f(x)]^(g(x)) is always increasing [f(x)]^(g(x)) is decreasing, when f(x) 1. If f(x)>1,t h e n[f(x)]^(g(x)) is increasing.

Suppose f(x)=e^(a x)+e^(b x) , where a!=b , and that f prime prime(x)-2f^(prime)(x)-15f(x)=0 for all xdot Then the value of (|a b|)/3 is ___

Discuss monotonocity of f(x)=x/(sinx)a n d g(x)= x / (tanx), w h e r e

If f(x)=|x-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)= ______ for x>2

Suppose that f(x) is differentiable invertible function f^(prime)(x)!=0a n dh^(prime)(x)=f(x)dot Given that f(1)=f^(prime)(1)=1,h(1)=0 and g(x) is inverse of f(x) . Let G(x)=x^2g(x)-x h(g(x))AAx in Rdot Which of the following is/are correct? G^(prime)(1)=2 b. G^(prime)(1)=3 c. G^(1)=2 d. G^(1)=3