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

If f(x)=4x-5 and g(x)=3^(x) , then f(g(2)) =

If f(x), g(x) be twice differentiable function on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 and g'(1)=6, f(2)=3, g(2)=9, then f(x)-g(x) at x=4 equals to:- (a) -16 (b) -10 (c) -8

Let f : {2, 3, 4, 5}-> {3, 4, 5, 9} and g : {3, 4, 5, 9} ->{7, 11 , 15} be functions defined as f (2) = 3 , f (3) = 4 , f (4) = f (5) = 5 and g (3) = g (4) = 7 and g (5) = g(9)=11. Find gof.

If g(x)=x^(2)+x-1 and g(f(x))=4x^(2)-10x+5 then find f((5)/(4))

If g(x)=3x-1 and f(x)=4g(x)+3 . What is f(2)?

If f: [-3,4] to R,f(x)=2x, " and " g :[-2, 6] to R,g(x) =x^(2) . Then find function (f+g)(x).

Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5) and let g (x) = f ^(-1) (x). Find g''(o).

Let f (x)=x+ (x ^(2))/(2 )+ (x ^(3))/(3 )+ (x ^(4))/(4 ) +(x ^(5))/(5) and let g (x) = f ^(-1) (x). Find g'''(o).

Given that f(x) = 4 x ^2 and g (x) =3-(x)/(2) , what is the value of f(g(4)) ?

if int_(0)^f(x) 4x^(3)dx=g(x)(x-2) if f(2)=6 and f'(2)=(1)/(48) then find lim_(x to 2) g(x)