Question

write the reciprocal of the following.

(-3)-1​

Answer 1

Answer:

This answer is trivial; it’s -1/3 but let’s try to find it in a better/funny way.

Hmm… what is the reciprocal of -3??? Well, what is first a reciprocal? We may need to call a definition:

A reciprocal of a number times a number is 1.

What would be another definition of a reciprocal?

A reciprocal of a number n is the coefficient of the inverse of the function f(x)=nx. An inverse of a function is the function with points swapped.

Let’s test f(x) = -3x. Check the points: (1, -3), (-1, 3)

Let’s find the coefficient of g(x) = mx. Check the points: (-3, 1), (3, -1)

Use the slope formula to find m: [math]\frac{-1–1}{3-(-3)}=\frac{-2}{3+3}=-\frac{2}{6}=-\frac{1}{3}[/math]. That is coefficient of our inverse function, and it’s also the inverse of -3.

(Good job asking this; it was a big, impossible journey.)

Answer 2

Answer:

1 - (-3)

because reciprocal I didd