Question

F(x) = x2 − 8x 15 g(x) = x − 3 h(x) = f(x) ÷g(x) h(x) = . The domain of h(x) is U

Answer 1

first blank is x-5

second blank is -infinity, 3

third blank is 3, infinity

Answer 2

h(x) = x - 5

set of all integers except 3

-∞ ≤ x ≤ ∞ and x ≠ 3

Explanation:

Given the two equations in the question

Equation 1

f(x) = x² − 8x + 15

Equation 2

g(x) = x − 3

To find equation 3 that is h(x) we need to divide f(x) by g(x)

f(x) / g(x)

x² − 8x + 15 / x − 3

By using quadratic factorisation

(x-3)(x-5) / (x-3)

Cancel (x-3) from both numerator and denominator

h(x) = x-5

The domain of h(x)

set of all integers except 3

-∞ ≤ x ≤ ∞ and x≠3