Question

F(x)=x^2+3x+6 and g(x)=x-3/2, solve for f(g(x)) when x=1

Answer 1

Do you have an idea of how to start?

Answer 2

You work from the inside out on these things. Begin with the inner function, g(x). Wherever you see an x in the g function, replace it with a 1. So, \[g(x)=x-\frac{ 3 }{ 2 }\]and replacing x with 1, you get\[g(1)=1-\frac{ 3 }{ 2 }\]The answer to that is -1/2. NOW replace the x in the f function with -1/2. That's the way the composite functions work. \[f(-\frac{ 1 }{ 2 })=(-\frac{ 1 }{ 2 })^{2}+3(-\frac{ 1 }{ 2 })+6\]That comes out to 19/4. And that's your answer! Study up on it so you know how to do it for the other ones; they are all done the same way, no matter what your functions are or how many of them there are. Work from the inside out.