Final answer:
To determine which pair of functions are inverses of each other, we need to check if the composition of the two functions gives us the identity function. The pair of functions that are inverses of each other is option D.
Step-by-step explanation:
To determine which pair of functions are inverses of each other, we need to check if the composition of the two functions gives us the identity function.
In other words, if we take one function, apply the other function to it, and end up with the original input, then the two functions are inverses.
Let's go through each option:
A. f(x) = y^3x and g(x) = (3)
These two functions are not inverses of each other because there is no way to apply g(x) (which is just a constant of 3) to f(x) (which is a variable raised to the power of 3 and then multiplied by x) and get back the original input.
B. f(x) = 12 + 15 and g(x) = 12x - 15
These two functions are not inverses of each other because the composition f(g(x)) gives us (12x-15) + 15 which simplifies to 12x, not the original input x.
C. f(x) = 11x - 4 and g(x) = 14
These two functions are not inverses of each other because the composition f(g(x)) gives us 11*14 - 4, which simplifies to 150, not the original input x.
D. f(x) = 3^-10 and g(x) = x + 10
These two functions are inverses of each other because the composition f(g(x)) gives us (x+10) to the power of -10. Using the property of exponents, we can simplify this to (1/(x+10)^10), which is the original input x.
Therefore, the pair of functions that are inverses of each other is option D.