Question

Operations with Functions

write the function below as either a sum/difference/product/quotient of 2 r more functions

a. h(x) = x^2+3x+9

How Would I do this? My teacher just did this

f(x) = x^2
g(x) 3x+9

^I don't really understand

h(x)=(x+5)(x-3)

how would I do this one?

If h(x) = x+2, write 2 different functions f(x) and g(x) such that:

a. f(x) + g(x) = h(x)
c. f(x) - g(x) = h(x)

Answer 1

f(x) + g(x) = (x^2) + (3x + 9) = x^2 + 3x + 9 = h(x)

you can break it into whatever pieces you like


h(x) = (x + 5)(x + 3) = x^2 + 8x + 15

f(x) = x^2 + 9 ; g(x) = 8x + 6

h(x) = f(x) + g(x)


a. f(x) = 3x - 1 ; g(x) = 3 - 2x
__ (3x - 1) + (3 - 2x) = x + 2 = h(x)

b. f(x) = 7x - 3 ; g(x) = 6x - 5
__ (7x - 3) - (6x - 5) = x + 2 = h(x)