If `f'(4)=5, f(4)=3, g'(6)=7` and `R(x)=g[3+f(x)]` then `R'(4)=`

If f(x)=f(4-x), g(x)+g(4-x)=3 and int_(0)^(4)f(x)dx=2 , then : int_(0)^(4)f(x)g(x)dx=

Suppose F(x)=f(g(x)) and g(3)=5,g'(3)=3,f'(3)=1,f'(5)=4 Then F'(3)=

f(x) and g(x) are two real valued function.If f'(x)=g(x) and g'(x)=f(x)AA x in R and f(3)=5,f'(3)=4 .Then the value of (f^2(pi)-g^(2)(pi)) is equal to

Let f:{2,3,4,5}rarr{3,4,5,9}a n d g:{3,4,5,9}rarr{7,11,15} be functions defined at f(2)=3,f(3)=4,f(4)=f(5)=5,g(3)=g(4)=7, a ndg(5)=g(9)=11. Find g(f(x))

Let f:R rarr R be defined as f(x)=x^(3)+3x^(2)+6x-5+4e^(2x) and g(x)=f^(-1)(x) ,then find g'(-1)

If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=

Consider f g and h are real-valued functions defined on R. Let f(x)-f(-x)=0 for all x in R, g(x) + g(-x)=0 for all x in R and h (x) + h(-x)=0 for all x in R. Also, f(1) = 0,f(4) = 2, f(3) = 6, g(1)=1, g(2)=4, g(3)=5, and h(1)=2, h(3)=5, h(6) = 3 The value of f(g(h(1)))+g(h(f(-3)))+h(f(g(-1))) is equal to

Suppose that h(x)=f(x)g(x) and F(x)=f(g(x)) where f(2)=3g(2)=5g'(2)=4f'(2)=-2 and f'(5)=11 then