Calculus Ap exam Questions 1975?

Question

Hey I am in Calculus right now and my teacher gave us this packet with questions from previous Ap exams.

1975 ABI

Given the function f defined by f(x)=ln(x^2-9)

(a) Descibe the symmetry of the graph of f.

(b) Find the domain of f.

(c) Find all values of x such that f(x)=0

(d) Write a formula for f^-1(x), the inverse function of f, for x>3.

I would really appreciate your help. I need answers by tonight, thanks.

-Also I need to show work so if you can show how you got it I would appreciate it, but if you know the answer I will accept that aswell, thanks.

Answer 1

a) it is a reflection symmetry about the y-axis
b) for f to be defined, x²-9 must be positive, which means |x|>3, so the domain of f is (-∞, -3) ∪ (3, ∞)
c) ln (x²-9) = 0 ⇒ x²-9=1 ⇒ x²=10 ⇒ x=±√10
d) y=ln (x²-9)
e^y = x²-9
e^y+9 = x²
x = √(e^y+9) (the positive square root is taken since x>3).

Therefore f⁻¹(x) = √(e^x+9)

Answer 2

(a) Domain: (0,∞) H(x) = ln((e^2x)^2) = ln(e^4x) = 4x (b) Domain: (0,∞) K(x) = e^(2ln(x^2)) = e^ln(x^2) * e^ln(x^2) = x^2 * x^2 = x^4 (c) y = ln(x^2) x = ln(y^2) e^x = y^2 ___ √e^x = y I'm not positive about the Domain... I believe it is either (0,∞) due to the restrictions for f(x) or (-∞,∞) because all real numbers provide a value for y.