Question

35. Explain the difference between the reciprocal of x^2

Answer 1

Answer:

As you can see, the difference between the reciprocal of $x^2$ and the inverse of   $x^2$ is that $\frac{1}{x^2} =x^{-2}$ and $\sqrt{x} =x^{\frac{1}{2}$.

Step-by-step explanation:

First lets find both the reciprocal of $x^2$ and the inverse of

Recall that the reciprocal of a value is where you take a fraction and swap the places of the terms. In the case of $x^2$, 1 is the denominator, so

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

To find the inverse of a function, you first need swap the locations of x and y in the equation

$y=x^2\\\\x=y^2$

Now, you need to solve for y

$y^2=x\\\\y=\sqrt{x}$

Now, lets rewrite each of these to better compare them

$\frac{1}{x^2} =x^{-2}\\\\\sqrt{x} =x^{\frac{1}{2}$

As you can see, the difference between the reciprocal of $x^2$ and the inverse of