Finding reciprocals of y=x² and y=√x and graphing them

[Raza]

What would be the reciprocal of the following:

$$A)y=x^2$$

$$B)y=\sqrt{x}$$

I think the reciprocal for A, it would be:

$$y=\frac{1}{x^2}$$

And B would be:

$$y=\sqrt{\frac{1}{x}}$$

And also, How would I graph this?
I just need the table of values. Well, I need to do domain,range,graphing and a summary but I think I can do that myself if I get how to do the table of values.


Thanks

 

[Gokul43201]

If you are talking about reciprocals of numbers, then yes, the reciprocals of $x^2~and~`\sqrt(x)~are~\frac{1}{x^2}~and~\frac{1}{\sqrt(x)}$

Since no domain has been provided in the question, you have to come up with what you think will be a relavant domain- ie : one which includes any "important" behavior.

For $y = x^2$, I would pick a bunch of numbers say, from the set [-10, 10].

 

[futb0l]

oops - lol nvm.

 

[Raza]

Would this be the graph:

The blue one is $$\frac{1}{x^2}$$ and the red one is $$\sqrt{\frac{1}{x}}$$

 

[HallsofIvy]

One question: since if f(x)= x² (for x>= 0), then f^-1(x)= &sqrt;(x) are the functions you give, are you sure it is "reciprocal" that is intended rather than the inverse function?

 

[Raza]

I don't get your question. Please rephrase it.

 

[Nylex]

I don't get your question. Please rephrase it.

He means are you sure you're meant to be doing 1/y or should you be finding the inverse function (eg. the inverse of multiplication is division, the inverse of squaring is square rooting)?

 

[Raza]

I am sure that I don't have to find the inverse function.