Final answer:
The multiplicative inverse of -4x is 1/4x, which is obtained by dividing 1 by -4x and simplifying to remove the negative sign from the denominator.
Step-by-step explanation:
The multiplicative inverse of a number is defined as a number which, when multiplied with the original number, will result in 1. Applying this definition, we want to find the multiplicative inverse of -4x. If we multiply -4x by its inverse, we should get 1:
(-4x) * (multiplicative inverse of -4x) = 1
Now, to find the inverse, we divide 1 by -4x:
1 / (-4x)
This simplifies to -1/4x. However, we want our answer to not have a negative sign in the denominator, so we multiply the numerator and denominator by -1 which gives us the positive inverse 1/4x, which is option c).