## mathmath333 one year ago functions.

1. mathmath333

\large \color{black}{\begin{align} &\normalsize \text{which of the following two functions are identical ?}\hspace{.33em}\\~\\ &a.)\ f(x)=\dfrac{x^2}{x} \ \hspace{.33em}\\~\\ &b.)\ g(x)=(\sqrt{x})^2 \hspace{.33em}\\~\\ &c.)\ h(x)=x \hspace{.33em}\\~\\~\\~\\ &i.) \ \normalsize a.) \ \text{and }\ b.)\hspace{.33em}\\~\\ &ii.) \ \normalsize b.) \ \text{and }\ c.)\hspace{.33em}\\~\\ &iii.) \ \normalsize a.) \ \text{and }\ c.)\hspace{.33em}\\~\\ &iv.) \ \normalsize a.),\ b.) \ \text{and }\ c.)\hspace{.33em}\\~\\ &v.) \ \normalsize \text{none of these } \hspace{.33em}\\~\\ \end{align}}

2. SolomonZelman

g is a line y=x for all x$$\ge$$0 f is a line y=x for all x, besides x=0 h is just a line y=x

3. triciaal

I got ii b) and c)

4. SolomonZelman

none of them are absolutely the same thing, but the closest ones I would say are f and h

5. Isaiah.Feynman

@Vocaloid for the first one, I think zero is not allowed the domain.

6. Vocaloid

^right, I didn't see that before, thank you

7. Vocaloid

so I would say that none of them are the same

8. SolomonZelman

you have almost got the absolute value in g, Absolute value definition: |D| = sqrt (D^2)

9. ParthKohli

None of them have the same domains!

10. SolomonZelman

but switching the order of ^2 and square root eliminates the left side of the absolute value function, making it y=x for all x>=0. (as I said before)

11. SolomonZelman

yes, none of them have the same exact domains

12. triciaal

I thought all the same but wanted 2

13. Vocaloid

the last option specifies "none of the above"

14. mathmath333

is the answer "none of these" as all are saying domain is not same.

15. ParthKohli

Yeah.

16. SolomonZelman

|dw:1434999703267:dw|

17. SolomonZelman

basically

18. triciaal

|dw:1434999855949:dw|

19. mathmath333

@SolomonZelman are u saying that f(x)=g(x) and option i) is correct ?

20. mathmath333

i mean * are u saying that f(x)=h(x) and option i) is correct ?

21. SolomonZelman

oh it shifted something

22. mathmath333

i mean option iii.) lol

23. SolomonZelman

|dw:1435000227558:dw|

24. SolomonZelman

is that better ?

25. mathmath333

ok option none of these thnks all

26. SolomonZelman

yup

27. SolomonZelman

$$\rm \color{green}{mathmath333=\left(math\right)^23^3=27\left(math\right)^2}$$

28. SolomonZelman

jk

29. mathmath333

hahaaaha