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

Question

1) describe the symmetry of the graph of f
2) find the domain of f
3) find all values of x such that f(x) = 0
4) Write a formula for the inverse function of f, for x>3.

Help Please

Answer 1

f(x) = ln (x^2 - 9)

1) f(-x)=f(x) --> A par symmetry
2) D= {x in R / x^2-9>0} = (-inf, -3) U (3,+inf)
3) f(x)=0 <--> ln(x^2-9)=0 <--> x^2-9=1 <--> x=±√10
4) For x>3 --> f↑ has inverse -->

y=ln(x^2-9) <--> e^y = x^2-9 <--> x^2=9+e^y <-->
x=±√(e^y+9) x>3>0

--> f^(-1) (x) = √(e^x+9)


Saludos.

Answer 2

f(x)= f(-x) sothere is symmetry with respect to the y axis.
-infinity zeroes at approximately -3.16 and 3.16
y= e^(x^2+9)