Answer:
As you can see, the difference between the reciprocal of [tex]x^2[/tex] and the inverse of [tex]x^2[/tex] is that [tex]\frac{1}{x^2} =x^{-2}[/tex] and [tex]\sqrt{x} =x^{\frac{1}{2}[/tex].
Step-by-step explanation:
First lets find both the reciprocal of [tex]x^2[/tex] 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 [tex]x^2[/tex], 1 is the denominator, so
[tex]\frac{x^2}{1} =\frac{1}{x^2}[/tex]
To find the inverse of a function, you first need swap the locations of x and y in the equation
[tex]y=x^2\\\\x=y^2[/tex]
Now, you need to solve for y
[tex]y^2=x\\\\y=\sqrt{x}[/tex]
Now, lets rewrite each of these to better compare them
[tex]\frac{1}{x^2} =x^{-2}\\\\\sqrt{x} =x^{\frac{1}{2}[/tex]
As you can see, the difference between the reciprocal of [tex]x^2[/tex] and the inverse of
