Let's Solve Some Math Problems!
What is the inverse of the function f(x) = 4x + 12?
Choose one:
- A. g(x) = 4x + 12
- B. g(x) = 4x - 12
- C. g(x) = 4x - 3
- D. g(x) = 1/4x - 3
Answer:
It's D.
Explanation:
In order to find the inverse of a function, we need to switch the input and output values. Given that f(x) = 4x + 12, we first need to make x the subject of the formula:
(f(x) - 12)/4 = x
x = 1/4f(x) - 3
By switching the input and output values, we find the inverse function g(x) = 1/4x - 3.
Understanding Inverse Functions
Inverse functions are a key concept in mathematics that involve reversing the input and output of a function. By finding the inverse of a function, we can determine the original input value when given the output value.
In the case of the function f(x) = 4x + 12, the inverse function g(x) is calculated as g(x) = 1/4x - 3. This process allows us to solve for the inverse function and understand the relationship between input and output values.
By mastering the concept of inverse functions, we can enhance our problem-solving skills and tackle more complex mathematical challenges with ease. So, keep practicing and exploring the world of mathematical functions!