Question

If r is a linear function with a non-zero slope, which of the following is always true of its inverse function?

A) It has a positive slope
B) It has a negative slope
C) It is also a linear function
D) It is a constant function

Answer 1

The inverse of a linear function with a non-zero slope is also a linear function; hence, Option C is correct.

Step-by-step explanation:

If r is a linear function with a non-zero slope, the inverse function will also be a linear function. This is because the inverse of a linear function with equation y = mx + b (where m is the slope and b is the y-intercept), assuming m is not equal to 0, is also a linear function with the form x = (1/m)y - (b/m), which rearranges to y = (1/m)x - (b/m). Thus, for the inverse function, the slope is 1/m which is also non-zero since m is not zero. Option C is always true - the inverse function is also a linear function.