Question

A function, f, is described by the following algorithm:

Start with a number, x, and multiply by 3
Subtract 10 from the result
Divide by 9
Which formula would be the inverse of this function?
a) f^(-1)(x) = 9 / (3x + 10)
b) f^(-1)(x) = (x + 10) / 3
c) f^(-1)(x) = 3x - 10
d) f^(-1)(x) = (3x + 10) / 9

Answer 1

The inverse of the function described by multiplying by 3, subtracting 10, and then dividing by 9, is the function that multiplies by 9, adds 10, and then divides by 3, which is formula b) f^(-1)(x) = (x + 10) / 3.

Step-by-step explanation:

The question concerns finding the inverse of a given function which is described by an algorithm. The steps of the function are: start with a number x, multiply by 3, subtract 10, then divide by 9. To find the inverse, we need to reverse these operations. We start with the final result which we can call y, and then we perform the inverse operations in reverse order:

1. Multiply y by 9 (inverse of dividing by 9).
2. Add 10 to the result (inverse of subtracting 10).
3. Divide by 3 (inverse of multiplying by 3).

Therefore, the formula for the inverse function is: f-1(x) = (9x + 10) / 3, which corresponds to option b) f-1(x) = (x + 10) / 3.