Asked by kieran
range and domain of f(x)=x^2-x-6/x-3 someone gave some input earlier but just looking to get a little more in depth help thanks
Answers
Answered by
Steve
The domain is the set of x values where f(x) is defined.
Since the numerator and denominator are both polynomials, their domains are all real numbers. However, we are dividing one polynomial by another, and division by zero is not defined. So, wherever (x-3) is zero, f(x) is not defined.
The domain of f(x) is thus all reals except x=3.
Now, x^2-x-6 is just (x-3)(x+2). So, except where x=3, f(x) = (x+2), and the range is thus all reals except 5, since f(x) is just a straight line, with a hole at (3,5).
Since the numerator and denominator are both polynomials, their domains are all real numbers. However, we are dividing one polynomial by another, and division by zero is not defined. So, wherever (x-3) is zero, f(x) is not defined.
The domain of f(x) is thus all reals except x=3.
Now, x^2-x-6 is just (x-3)(x+2). So, except where x=3, f(x) = (x+2), and the range is thus all reals except 5, since f(x) is just a straight line, with a hole at (3,5).
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