## suss 2 years ago find the domain y=f(x)=x^2-6x+6

1. hartnn

domain means the values which 'x' can take in that equation.

2. hartnn

do u see any values that 'x' can't take ?

3. suss

i dont get it......??

4. hartnn

(1)there is no denominator, if there was, then 'x' could not take values for which denominator=0

5. suss

so ther is no soln for this??

6. hartnn

(2) there is no $$\sqrt.$$ sign, if there was , then 'x' cannot take values for which the expression under $$\sqrt{...}$$becomes negative.

7. hartnn

here, none of the 2 cases (1) or (2) arise. so 'x' can take all real values.

8. hartnn

so, domain is ALL real numbers R

9. hartnn

understood ?

10. suss

sorry i quite didnt get it

11. hartnn

which par ?

12. suss

x belongs to R then can we supoose any no we want in the place of x??

13. hartnn

yes, x can take any real value. u have options/choices ?

14. suss

how wud u solve this prob?

15. hartnn

example : f(x) =1/ x x cannot take value =0 f(x) = 1/(x-3) x cannot take value = 3 f(x) = sqrt{x-4} x cannot take value less than 4

16. suss

can u be mo` specific...?i cant understand

17. hartnn

i just gave u specific examples. and there's nothing to solve, you can say 'x' can take all real values...

18. suss

y did u add -3 in da denominator?

19. ParthKohli

By the way, all polynomials have the domain $$(-\infty,\infty)$$ a.k.a $$\mathbb{R}$$.

20. suss

can u do the whole process??

21. BluFoot

Domain means whenever the function exists. To figure this out, just find when the function does not exist, meaning when you're dividing by 0. In this case, you're never dividing by 0, so the function ALWAYS exists, so the domain is ]-inf,inf[, also know as "R" for all real numbers. If say f(x) = 1/(x-4), then the domain is ]-inf,-4[U]-4,inf[, because the function exists everywhere except at x=-4.