Name: Mina

Who is asking: Student
Level: Secondary

Question: I have tried this question, but I always get stuck!

Let f(x) = (2x2+3x-17)/(x+5)
What is the domain of f? What are the values of x for which f'(x) does not = 0?

Thank-you for your help,
Mina :)

Hi Mina,

Imagine that you have a button on your calculator labeled (2x2+3x-17)/(x+5). It works like the square root button. Input a number, call it x, then press this button and the calculator shows the value of (2x2+3x-17)/(x+5). For what values of x does this button give an error message?

I know that my calculator gives an error message if I

1) try to take the square root of a negative.

or

2) try to divide by zero. There are no roots in (2x2+3x-17)/(x+5) so the only error would come from trying to divide by zero. That is when x+5 = 0. Hence x = -5. Thus the function f works properly for all x except x = -5 and hence the domain of f is all rreal numbers except x = -5.

For the second part I would first find all x for which f'(x) = 0.

Cheers,
Harley
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