Final answer:
The characteristic always true of the inverse function of a linear function with a non-zero slope is that the slope of the inverse is the reciprocal of the original function's slope. Therefore correct option is A
Step-by-step explanation:
If r is a linear function with a slope that is not equal to zero, the characteristic that is always true of its inverse function is that the slope of the inverse is the reciprocal of the slope of r.
This can be understood by considering the slope-intercept form of a linear equation, which is y = a + bx, where b represents the slope and a represents the y-intercept.
When a function f(x) with slope b is inverted to form f-1(x), the slope of the line representing f-1(x) must be the reciprocal of b to maintain the property that f(f-1(x)) = x.
Thus, if the slope of r is not zero, its inverse will not be a horizontal line (which would represent a zero slope), and the slope must indeed be the reciprocal of the slope of r.