1. Given that f(x) = x^2 − 2x and that g(x) = sqrt(x-15):
A. State (g • f)(x) and (g + f)(x).
B. Find all vertical asymptotes of (g/f)(x).
C. Determine the domain of (g ○ f)(x).
D. Determine the range of (g ○ f)(x).
2 answers
No calculators are allowed for this question.
(g • f)(x)
= √(x-15)(x^2-2x) , can you see what I did?
now do the same for (g+f)(x)
similarly , (g/f)(x) = √(x-15)/(x^2 - 2x)
B) for VA's the denominator is zero
so when is x^2 - 2x = 0
x(x-2) = 0
x = 0 and x = 2 are the vertical asymptotes
C)
(g ○ f)(x)
= g(f(x) )
= g(x^2-2x)
= √((x^2-2x)-15)
= √((x-5)(x+3)
domain is your choice of x's that you may use in the expression to yield a real number.
Clearly the inside of the square root has to be ≥ 0
this is true for x ≤ -3 OR x ≥ 5
D) repeat my method of C), remember that range is the resulting output from your function, that is , your y values.
= √(x-15)(x^2-2x) , can you see what I did?
now do the same for (g+f)(x)
similarly , (g/f)(x) = √(x-15)/(x^2 - 2x)
B) for VA's the denominator is zero
so when is x^2 - 2x = 0
x(x-2) = 0
x = 0 and x = 2 are the vertical asymptotes
C)
(g ○ f)(x)
= g(f(x) )
= g(x^2-2x)
= √((x^2-2x)-15)
= √((x-5)(x+3)
domain is your choice of x's that you may use in the expression to yield a real number.
Clearly the inside of the square root has to be ≥ 0
this is true for x ≤ -3 OR x ≥ 5
D) repeat my method of C), remember that range is the resulting output from your function, that is , your y values.
1 answer