Question

Find the domain of the function. x^4/x^2+x-6

Answer 1

For this:

Factorize the denominator..
Can you do it?

Answer 2

Make the factors of:

\[x^2 + x - 6\]

Answer 3

And first of all:

\[\huge \color{green}{\textbf{Welcome To Openstudy..}}\]

Answer 4

ok i got the factors... (x+3) and (x-2) right?

Answer 5

Yes very right dear...

Now you know if x = -3 then what will be the value of function??
Put x = -3 in the function..

Can you determine the value??

Answer 6

Or you can simply say that:

Denominator should be not be Zero..
Otherwise the Function becomes Undetermined..

\[Denominator \ne 0\]

Getting it or not??

Answer 7

Or simply substitute the value of Denominator in that equation I have just written above:

\[(x+3)(x-2) \ne 0\]

Find x from here...

Answer 8

yea i get the part of it being undefined because the zero cant be a denominator but i got confused where you told me to find the value...

Answer 9

so x cannot equal -3 or +2?

Answer 10

Yes you are going very right..

So, x can take any value except -3 and 2...

Right??

Answer 11

So, domain will be All Real Numbers except 2 and -3..

We represent it as:"

\[Domain : \mathbb{R} - (-2, 3)\]

Getting or not??

Answer 12

ok then so the numerator has nothing to do with the domain?

Answer 13

No no..
Domain tell us the value of x for which the function is determined or undetermined..

Answer 14

ok then i get it know!:) thanks

Answer 15

Welcome dear..