If f(x)=4 x+1 and g(x)=k x+2 such that f g(x)=g f(x) , then what is the value of k ?

Step-by-step solution

aligned & Given, f(x)=4 x+1, g(x)=k x+2 & fog (x)=4(k x+2)+1=4 k x+9 & go f(x)=k(4 x+1)+2=4 k x+k+2 & fog (x)=g of (x) g=k+2 k=7 aligned