Question

Find the Domain and range of f(x) = ln(x^2-2x-3)

I am slightly confused by the question, as to solve the quadratic it must be equal to zero, but ln x must be greater than zero.

This is my working before I discovered this error
f(x)=ln(x^2-2x-3)
(x^2-2x-3)=parabola
Domain of a parabola=All real numbers
Domain of f(x)=ln(x)= >0
D:{All real numbers>0}

Range: (x,y)
x^2-2x-3=ax^2+bx+c
x=(-b)/2a
b= -2
a=1
x=(-(-2))/2(1)
x=1
y=f(x)=ln(x^2-2x-3)
y=f(1)=ln(1^2-2(1)-3)
y=ln(1^2-2(1)-3)
=ln(-4)
y=undefined
Range: (1,undefined)

Is this acceptable?

Answer 1

That looks good. The only thing is, the (1,und.) 1 is confusing. It looks as though you're using interval notation, so simply say the range is undefined, as the x value has no place there

Answer 2

Thank you :)

Answer 3

No problem

Answer 4

when I solved the quadratic the values were -1, 3 this is when f(x) = 0
-b/2a is used to find the x value of the vertex when f(x) is at a minimum