Can someone check this? Thanks! :)
Which pair(s) of functions are inverses? There may be more than one correct answer.
a.) f(x) = x - 12, g(x) = x + 12
b.) f(x) = 3x, g(x) = 1/3x
c.) f(x) = 4x, g(x) = -4x
d.) f(x) = 2x + 1, g(x) = 2x - 1
My answer: A & C
To determine which pair(s) of functions are inverses, we need to check if applying one function and then the other will result in the original input.
Let's check each option:
a.) f(x) = x - 12, g(x) = x + 12
To find the inverse of f(x), we need to solve for x:
x = f(x) + 12
x = (x - 12) + 12
x = x
So, g(x) is indeed the inverse of f(x).
b.) f(x) = 3x, g(x) = 1/3x
To find the inverse of f(x), we need to solve for x:
x = f(x) / 3
x = 3x / 3
x = x
So, g(x) is indeed the inverse of f(x).
c.) f(x) = 4x, g(x) = -4x
To find the inverse of f(x), we need to solve for x:
x = f(x) / 4
x = 4x / 4
x = x
So, g(x) is indeed the inverse of f(x).
d.) f(x) = 2x + 1, g(x) = 2x - 1
To find the inverse of f(x), we need to solve for x:
x = (f(x) - 1) / 2
x = (2x + 1 - 1) / 2
x = 2x / 2
x = x
So, g(x) is indeed the inverse of f(x).
Based on the above analysis, options a, b, c, and d all have inverses. Therefore, there is more than one correct answer. Your answer of A & C is correct.