composition of functions

Question

can someone explain this to me? If h(x) = 6 – x, what is the value of (h*h)(10)

Answer 1

If h(x) = 6-x, we can use the substitution property for any h we see in a composite function.

 

Therefore, we can rewrite (h*h)(x) as (6-x)(6-x).

 

Multiplication of polynomials tells us that we must distribute each term in one of the polynomials across the other polynomial when we multiply. Therefore, when we simplify, we get:

 

36 - 6x - 6x + x²

36 - 12x + x²

 

Now, we calculate the function for the given value, which was 10.

 

36 - 12(10) + 10²

36 - 120 + 100 = 16

 

So we have a final answer of 16.