Question

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

and the inverse of x^2. (number 35 in the pic)

Answer 1

As you can see, the difference between the reciprocal of
`x^2` and the inverse of
`x^2` is that
`(1)/(x^2) =x^(-2)` and
`√(x) =x^{(1)/(2)`.

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

`(x^2)/(1) =(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=√(x)`

Now, lets rewrite each of these to better compare them

`(1)/(x^2) =x^(-2)\\\\√(x) =x^{(1)/(2)`

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