Is X (squared) the inverse of the square root of x?

Question

And how or why?

Answer 1

Not exactly.

If you graph the function f(x) = x^2, you'll notice that it's a parabola, right? You'll also notice that it is not one-to-one, because it fails the horizontal line test, and thus is not a function.

We use our normal methods to calculate the inverse of the square root of x:

let y = sqrt(x).

To solve for the inverse, we switch the terms x and y, and then solve for y.

x = sqrt(y)

Square both sides

x^2 = y, or y = x^2.

So at this moment, it would appear that x^2 is the inverse of sqrt(x). However, for y = sqrt(x), the x values are restrictives such that x >= 0.

Therefore, the *ACTUAL* inverse of sqrt(x) is x^2, where x >= 0.

f(x) = sqrt(x)
f^(-1)(x) = x^2, x >= 0

If you graph f^(-1)(x), you'll see that it's half of a parabola, BUT it is one-to-one like all inverse functions should be.

Answer 2

X must be greater than or equal to 5. Explanation: To start off with, if X equals 5, you will have 5-5=0, and you can take the square root of that. you can take the square root of any number that is not a negative value. Even though 0 is neither positive nor negative (it is in the middle), you can still take it's square root. As for X being greater than 5, we will use X=6 as an example. 6-5=1 ---> and the square root of 1 is 1. Last example: X=9 9-5=4 ---> the square root of 4 is 2. ALTHOUGH: if you X value was equal to zero, you would have 0-5= -5, which does not work, because you cannot take the square root of a negative number. Also, for the part that says X is greater than 0, it is partially valid, but only if the X value is greater or equal to 5. EXAMPLE: X=3 Although, 3 is greater than 0, it is still less than 5. 3-5= -2, you cannot take the square root of -5. So the answer is the 2nd one: X is greater than or equal to 5. I hope you get it now :)

Answer 3

No...X squared = X x X
square root of X = X to the power of 1/2...
the inverse of square root X is then X to the power of - 1/2, which does not = X x X...

Answer 4

The inverse of x^2 is written = (x^2)^(-1), which is x^(2*-1) or x^(-2) which is 1/(x^2) and not the square root of x.

Similarly, sqrt(x) is x^(1/2) and the inverse is (x^(1/2))^(-1) or x^(1/2*-1) or x(-1/2) which is 1/(sqrt x) and not x^2.

Answer 5

yes it is just like finding the square root ( sqrt ) f any integer

example : find the sqrt of 4

solution :

sqrt ( 4 ) = 2 you check this as you do any sqrt by finding what " x " Sqt is

x ^2 = x times x just as
2 ^2 = 2 times 2 = 4

Answer 6

No.
let us take a number say 4
square root is 2
square of the number is 16
so They are not inverse.
In fact [sqrt x]^4=x^2

Answer 7

Yes and no.

sqrt(x²) = |x|
As you can see, x² will always give a positive result, and sqrt(x) will also always give a positive result.

So, for positive numbers, x² is the inverse of sqrt(x). For negative numbers, x² is not the inverse of sqrt(x).

Answer 8

f(x)= y = x^2
The inverse is:
x = y^2, solved for y.
y = (+/-) sqrt(x)

Since y yields two values for x, it isn't a function.

Answer 9

Yes.

Answer 10

Yes, it is the reciprocal