To determine which two parent functions are inverses of each other, let's review each function and its possible inverse.

1. Linear function: The inverse of a linear function is also linear (if the slope is non-zero), but this function isn't paired with any other type in the list.

2. Cubic function: The inverse of a cubic function is the cube root function, but a cube root function isn't listed.

3. Logarithmic function: The inverse of a logarithmic function is the exponential function.

4. Square root function: The inverse of a square root function is the quadratic function, but quadratic is not listed here.

5. Exponential function: As noted, the inverse of an exponential function is the logarithmic function.

6. Rational function: This function doesn't have a straightforward inverse in the list.

Thus, logarithmic (C) and exponential (E) are the two functions that are inverses of each other.

Do you want more details or have any questions?

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Relative questions:

1. How do you find the inverse of a cubic function?
2. Can a rational function ever be its own inverse?
3. How can you graphically verify that two functions are inverses of each other?
4. What is the general form of an exponential function?
5. What happens to the domain and range when you invert a logarithmic function?

Tip: The graph of a function and its inverse is symmetric across the line $y = x$.