I came across this problem in a text I am using currently and was confused by the notation and am not sure of the answer

given a function $\displaystyle f = h(g_1, g_2, g_3)$

if $\displaystyle h=x^2 - yz$ and $\displaystyle f = h(x+y, y^2,x+z)$ then is it correct to apply the pointwise vector coordinate function and get $\displaystyle f = (x+y)^2 -y^2(x+z)$

This seemed like a trivial problem but the notation really confuses me.