let f(x)=x+3 and let g(x)=(sqrt(x))+9 (i) solve f of g (ii) solve g of f Are the following answers correct? (i) (sqrt(x))+12 (ii) (sqrt(x)+3)+9
f of g is replacing g for x in f(x), so f(g(x)) = (sqrt(x)+9) + 3 = sqrt(x)+12 (i), so yes it is correct.
g(f(x)) = sqrt(x+3) + 9 (ii) Be sure to remember x+3 goes inside the square root.
