SOLUTION: domain and range of: 5+log(base 3) (x^2-2x-3)

Question 715792: domain and range of:
5+log(base 3) (x^2-2x-3)
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
.......to find a domain and range you need to solve quadratic equation using quadratic formula

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-2, and c=-3

Negate -2 to get 2

Square -2 to get 4 (note: remember when you square -2, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

since roots are and ,
the domain is

the range is:

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