Which represents the inverse of the function f(x) = 4x?

Question: Which represents the inverse of the function f(x) = 4x?

A) f(x) = 4/x
B) f(x) = x/4
C) f(x) = -4x
D) f(x) = x + 4
Answer: B) f(x) = x/4
Explanation: The inverse of a function is a function that undoes the original function. In other words, if we apply the inverse function to the output of the original function, we get back the input value.
To find the inverse of the function f(x) = 4x, we need to solve for x in terms of y and then swap the x and y variables.
Starting with the original function f(x) = 4x:
y = 4x
Dividing both sides by 4:
y/4 = x
Now, swapping x and y, we get:
x/4 = y
Therefore, the inverse of the function f(x) = 4x is given by:
f^-1(x) = x/4
Option B, f(x) = x/4, is the correct answer as it represents the inverse of the given function f(x) = 4x. Option A, f(x) = 4/x, is the inverse of f(x) = 1/(4x). Option C, f(x) = -4x, is the reflection of f(x) = 4x about the y-axis, and option D, f(x) = x + 4, is an unrelated function.

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