Find the composition

Question

If f(x)=x²+6x and g(x)=x+4, find (f·g)(2)

Answer 1

Cathryn,

 

When you have composition of two or more functions just evaluate from right to left.  In your case of 2 functions composed with g on the right, first evaluate g(x) for x = 2 to get y the dependent variable, then evaluate f using the computed y as its independent variable argument.  So

 

g(x) = x + 4 , then y = g(x=2) = (2 + 4) = 6  and now ignoring the original given value of x=2, we rewrite the function  f using y as its argument (i.e, y=x):

f(y)  = y² + 6y,  and for the computed y = 6 earlier, f(y) = (6)² + 6(6) = 36 + 36 = 72.

Your answer:  [f o g](2) = 72.

 

If there were more than 2 functions being composed, like linked elephants in a circus line, just keep working leftward using the latest calculated dependent variable value as the independent variable for the next function on the left.