If f(x) = 5x + 3 and g(x) = 2x + 3, what is f(g(x)) ?

Question

anonymous · Answer

A) 10x + 21

B) 10x + 18

C) 10x + 15

D) 10x + 12

whpalmer4 · Answer

If $f(x) = 5x+3$ and $g(x) = 2x+3$ we can find $$f(g(x)) = f(2x+3) = 5(2x+3) + 3$$we just rewrite the outer equation substituting the right hand side of the inner equation as the argument of the function.  Think of the functions as patterns, and if the multiple uses of the same letter confuse you, rewrite like this:
$$f(u) = 5u + 3$$$$g(x) = 2x+3$$$$f(g(x)) = 5u + 3 = 5(g(x))+3 = 5(2x+3) + 3$$

anonymous · Answer

so itll be 10x+18 ?

whpalmer4 · Answer

$$5(2x+3)+3 = 5*2x + 5*3 + 3 = 10x + 15 + 3 = 10x + 18\checkmark$$

whpalmer4 · Answer

You can check this numerically, too.  Pick a number, any old number.  x=3, for example:
g(3) = 2x+3 = 2*3+3 = 6+3 = 9
f(g(3)) = f(9) = 5x+3 = 5*9+3 = 45+3 = 48

Now check against our formula:
f(g(3)) = 10x + 18 = 10(3)+ 18 = 30 + 18 = 48

so it checks out.  I'd do more than one point if we had a more complicated set of equations, but you get the idea, I hope.