Functions, f and g are given by f(x)= 3+ cos x and g(x) = 2x, x is a real number. Determine the value of c for which f(g(x))= g(f(x)) where 0x<2

The value x is equal to for which f(g(x))=g(f(x))

Given :

f(x)=3+cos(x)

g(x)=2x

To find : the value of x over the given interval

Apply composition of functions. Replace g(x) inside f(x) to find f(g(x))

Now we set f(g(x))=g(f(x)) and solve for x

cos(x)=2 cannot be solved , so no solution

Learn more :  

b

step-by-step explanation: