Question

Given f(x) = 3x, g(x)=x-4, and h(x)=x², what is (h*(f-g))(2)?

(h*(f-g))(2)=________.

a) 10
b) 20
c) 32
d) 64

Answer 1

To find (h*(f-g))(2), we need to calculate the values of f-g and substitute it into h. The result is 64.

Step-by-step explanation:

To find (h*(f-g))(2), we need to first calculate the values of f-g and then substitute it into h. We can find f-g by subtracting the values of g from f:

(f-g)(x) = (3x) - (x-4) = 2x+4

Now we substitute this into h:

(h*(f-g))(x) = h((2x+4)) = (2x+4)^2 = 4x^2 + 16x + 16

To find (h*(f-g))(2), we substitute x = 2 into the expression:

(h*(f-g))(2) = 4(2)^2 + 16(2) + 16 = 4(4) + 32 + 16 = 16 + 32 + 16 = 64

Therefore, (h*(f-g))(2) equals 64.