# What is the inverse operation of a quantity to the 2nd power?

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• You can use exponential rule to figure it out

(F^2)^x= f ^(2x)

You can then find when the exponent = 1

2x =1

X= 1/2

• y = x^2 hence x = y^(1/2) ;that is the 'square root' of 'y'.

• You are asking for the inverse function of x².  That function is not injective, so it cannot have an inverse.

Given x²,  the inverse function, if it existed, would return a unique x. That is possible only if x² = 0.

• f(x) = x²

// Find the inverse f⁻¹(x):

STEP 1. Rename f(x) to y:     y = x²

STEP 2. Swap variables:       x = y²

STEP 3. Solve for y:               y = ±√x

STEP 4. Rename y to f⁻¹(x):   f⁻¹(x) = ±√x

The inverse operation of taking the square of a quantity is taking the square root of the quantity. • Anonymous
4 months ago

x^2 and 1/x^2 maybe

• It is not at all clear what the question means.

What is an "operation of a quantity";

and what does the second power apply to?

• suppose y=x^2

if x>=0 then x=y^0.5

if x<0 then x=-y^0.5