Which function has an inverse that is a function?A) b(x) = x2 + 3 B) d(x) = –9 C) m(x) = –7x D) p(x) = |x| 

C) m(x) = –7x has an inverse that is also a function.

Here's the reasoning for each option:

A) b(x) = x^2 + 3 - This function does not have an inverse that is a function because it is not one-to-one. For every y value there are two x values (one positive and one negative), thus its inverse would not pass the horizontal line test.

B) d(x) = –9 - This is a constant function, and its graph is a horizontal line. Because every x-value is mapped to the single y-value of -9, if you tried to find an inverse, you would not have a function, since functions require each x value to be mapped to exactly one y value.

C) m(x) = –7x - This is a linear function with slope -7 and no y-intercept. Linear functions with non-zero slopes are always one-to-one and therefore always have inverses that are also functions. The inverse of this function would be a linear function with a slope of -1/(-7), or 1/7.

D) p(x) = |x| - The absolute value function is not one-to-one because for every positive y value, there are two x values (one positive and one negative). Therefore, its inverse would not pass the horizontal line test and thus is not a function.