finding the domain of the rational function.

Question

f(x)=x^2-36/x^2-7x+6
Thanks.

Answer 1

The function is f(x) = (x² - 36)/(x² - 7x + 6).

Find the factors of denominator expression x² - 7x + 6.

= x² - 6x - x + 6

= x(x - 6) - (x - 6)

= (x - 1)(x - 6)

Find the factors of numerator expression x² - 36.

= x² - 6²

Apply difference of squares : a² - b² = (a + b )(a - b ).

= (x + 6)(x - 6).

f(x) = (x² - 36)/(x² - 7x + 6) = [(x + 6)(x - 6)] / [(x - 1)(x - 6)] = (x + 6) / (x - 1).

f(x) = (x + 6) / (x - 1).

Domain excludes x - values that result in division by zero.

The function has an implied domain that consists of all real x other than x = 1.This value is excluded from the domain because division by zero is undefined.