Multiplying two functions results in h(x) = 10x2 + 12x – 16, while adding the same functions results in j(x) = 7x. which statements describe f(x) and g(x), the original functions? select two options. both functions must be linear. both functions must be quadratic. both functions must have a y-intercept of 0. the rate of change of either f(x) or g(x) must be 0. the y-intercepts of f(x) and g(x) must be opposites.

Both functions must be linear

The y-intercepts of f(x) and g(x) must be opposites

Step-by-step explanation:

* Lets study the problem

- The product of f(x) and g(x) = h(x)

∵ h(x) is a quadratic

* Both functions must be linear

- We can factorize h(x) into two linear factors

∵ h(x) = 10x² + 12x - 16

- The sign of the last term is negative, the factors have different sign

∵ 10x² = 5x × 2x ⇒ 1st numbers in the two brackets

∵ -16 = 4 × -4 ⇒ 2nd numbers in the two brackets

∵ 5x × 4 = 20x ⇒ 1st number in the first bracket and 2nd number

  in the second bracket

∵ 2x × -4 = -8x ⇒ 1st number in the second bracket and 2nd number

  in the first bracket

∵ 20x - 8x = 12x ⇒ middle term of h(x)

∴ The factors of h(x) are (5x - 4)(2x + 4)

* f(x) = 5x - 4 and g(x) = 2x + 4

- The adding of the two factors is j(x)

∵ f(x) + g(x) = 5x - 4 + 2x + 4 = 7x

∵ The y-intercept of f(x) = -4

∵ The y-intercept of g(x) = 4

∴ The y-intercepts of f(x) and g(x) are opposites

* The y-intercepts of f(x) and g(x) must be opposites

5y

step-by-step explanation: