SOLUTION: Can you help me with this question?: Find the domain and range of a function: f(x)= 3ln(6-2x) and solve the equation: f(x^2-2) = 0 I have tried this: 6-2x > 0 -2x > -6

Algebra ->  Functions -> SOLUTION: Can you help me with this question?: Find the domain and range of a function: f(x)= 3ln(6-2x) and solve the equation: f(x^2-2) = 0 I have tried this: 6-2x > 0 -2x > -6       Log On


   

Question 991061: Can you help me with this question?: Find the domain and range of a function:
f(x)= 3ln(6-2x) and solve the equation: f(x^2-2) = 0
I have tried this:
6-2x > 0
-2x > -6
x < 3 ...(-∞, 3) as a domain of this function?
Thank you!
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
Find the domain and range of a function

f(x)= 3ln(6-2x).

I have tried this:
6-2x > 0
-2x > -6
x < 3 ...(-∞, 3) is the domain of this function?
----------------------------------------------------------------

You are absolutely right regarding the domain!

Good job!

The range of this function is the entire number line (all real numbers).


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:f%28x%29=+3ln%286-2x%29 and solve the equation: f%28x%5E2-2%29+=+0
f%28x%29=+3ln%286-2x%29
f%28x%29=+3ln%282%283-x%29%29solve the equation: f%28x%5E2-2%29+=+0
f%28%28x%5E2-2%29%29=+3ln%282%283-%28x%5E2-2%29%29%29=0
+3ln%282%283-x%5E2%2B2%29%29=0
+3ln%282%285-x%5E2%29%29=0
domain: will be all values of x that make
5-x%5E2%3E0+ because ln is not defined for values <=0
5%3Ex%5E2
sqrt%285%29%3Ex
sqrt%285%29%3Ex
-sqrt%285%29%3Cx
{ x element R : -sqrt%285%29%3Cx%3Csqrt%285%29 }