h(x)=x^2-4x g(x)=3x-3 Find (h*g)(1)

Answer 1

My guess is that by (h * g) (1), you meant (h ⸰ g) (1) (alternatively written as h (g(1))

(h ⸰ g) (x) is a nested function:

General solution: Wherever there is an “x” in h(x), replace it with (3x – 3), which is the value of g(x):

    (h ⸰ g) (x) = (3x – 3)² – 4 (3x – 3)

                     = 9x² – 18x +9 – 12x + 12

                     = 9x² – 30x + 21

 For x = 1:

     (h ⸰ g) (1) = 9 – 30 + 21 = 0

Alternative solution method:

   Solve for g(1):  g (1) = 3(1) – 3 = 0

    Insert this value into h(x):  h (0) = 0² – 4(0) = 0

   

Answer 2

Given: h(x)=x²-4x g(x)=3x-3

What we want to find: (h*g)(1)

Work:

(h*g)(x)=(h(x))(g(x))

(h*g)(x)=(x²-4x)(3x-3)

(h*g)(x)=3x³-15x²+12x

(h*g)(1)=3(1)³-15(1)²+12(1)

(h*g)(1)=3-15+12 = 0

Solution:

(h*g)(1)=0

In this question just make sure that you find h*g with respect to x first. Do not do h(1)*g(1).

I hope this answered your question is as much detail as you needed!