Let f(x) = x2 − 5x + 7 and g(x) = x2 − 3x + 2. Find the function.

Question

f/g =

Find the domain. (Enter your answer using interval notation.)

Answer 1

To find f/g:

f(x)/ g(x) = (x² − 5x + 7) / (x² − 3x + 2)

Domain is all possible values that can exist for this equation. One limitation is that a fraction cannot have 0 in the denominator. So we need to find which x values would make the denominator equal 0 and exclude those from the domain.

1st: factor g(x)

x2 − 3x + 2 = (x - 2)(x - 1)

2nd: set it equal to 0 and solve for x

(x - 2)(x - 1) = 0

x - 2 = 0 Or x - 1 = 0

x = 2 Or x = 1

So our domain is anything less than 1, between 1 and 2, and anything greater than 2

(-∞, 1) ∪ (1,2) ∪ (2, ∞)

Answer 2

g(x) = (x-1)*(x-2)

The solutions are the additive inverses of the factors, so:

The domain is (-∞,1)∪(1,2)∪(2,∞).