Given that f(x)= x^2-2x and that g(x)=sqrt(x-15)

Question

A. State (g • f) (x) and (g+f) (x)

B. Find all vertical asymptotes of (g/f) (x)

Answer 1

A) (g • f) (x) = g(x) • f(x). This means you take g(x) and multiply it by f(x). It looks like this: (x²-2x)(√x-15)

(g + f) (x) = g(x) + f(x). This means you add g(x) and add it to f(x). It looks like this: x² - 2x + √x-15

B) (g/f) (x) = g(x) / f(x) = √x-15) / x² - 2x

Vertical Asymptotes is when your denominator = 0.

Set x² - 2x = 0 then factor

x (x - 2) = 0

x = 2 and x = 0

Therefore, the vertical asymptotes are x = 0 and x = 2.

Answer 2

g+f = x^2 - 2x + sqrt(x-15)

g*f = (x^2-2x)(sqrt(x-15))

g comp f = (x-15) - 2 * sqrt(x-15)

g/f = (x^2-2x)/sqrt(x-15)

the domain:

x-15>0

x>15