## anonymous 5 years ago Why would f(1/4) be undefined?

1. Anikate

well we no that the answer is f/4

2. Anikate

there is no equal sign

3. asnaseer

your question is not complete. you need to tel us what f(x) is defined to be.

4. anonymous

I have to explain why why f(1) = 3, f(0) = 2, and f(-1) = 1, but why f(1/4) is defined

5. anonymous

*undefined

6. asnaseer

have you been given the expression for f(x) in terms of x?

7. anonymous

in the 4x^2+ 7x - 2/ 4x-1

8. asnaseer

ok - now it makes sense

9. anonymous

i simplified it to x + 2/ 1 XD

10. asnaseer

if you look at the last term, you have a division by "4x-1". what will "4x-1" equate to when x=1/4?

11. asnaseer

$f(x)=4x^2+7x-\frac{2}{4x-1}$

12. anonymous

ohhh it would be 0

13. asnaseer

correct - so you would be dividing by zero - which is undefined.

14. asnaseer

BTW: your simplification to x + 2/ 1 is not correct.

15. anonymous

ahhhh :( what I do wrong?

16. asnaseer

can you please try and explain to me step by step what you did so that I can spot where you went wrong

17. anonymous

I factored to get (x+2)(4x-1)/4x-1 then canceled out common factors and got x+2/1

18. asnaseer

your factorisation in wrong. remember the last term is a fraction.

19. asnaseer

\begin{align} f(x)&=4x^2+7x-\frac{2}{4x-1}\\ &=\frac{(4x-1)(4x^2+7x)-2}{4x-1} \end{align}

20. anonymous

its supposed to be a rational expression o.O

21. anonymous

it looks like this : 4x^2+ 7x - 2 -------------- 4x-1

22. asnaseer

so the equation is supposed to be:$f(x)=\frac{4x^2+7x-2}{4x-1}$

23. asnaseer

which can be factored as:$f(x)=\frac{(x+2)(4x-1)}{4x-1}$

24. anonymous

yes :)

25. asnaseer

but you cannot cancel the 4x-1 because it would be like dividing top and bottom by zero when x=1/4

26. anonymous

i just canceled out common factors that what my teacher told me :(

27. asnaseer

you can only do that if you are told that x can NEVER be equal to 1/4

28. asnaseer

in this case I believe x can take on ay real value from minus infinity to plus infinity

29. asnaseer

and it is undefined at x=1/4

30. asnaseer

was the question asking you why is this undefined at x=1/4?

31. anonymous

yes

32. asnaseer

so then you can state that it undefined at x=1/4 because at x=1/4 we would be dividing by zero.

33. anonymous

okay Thank you!!! XD Wish i could giv you more than one medal o.O lol

34. asnaseer

You're welcome - I'm glad I was able to explain it well enough for you.