Final answer:
The correct inverse function of f(x) = 5x is f ⁻¹(x) = x/5, obtained by interchanging x and y and then solving for y to express y as a function of x.
Step-by-step explanation:
The correct answer is option f ⁻¹(x) = x/5.
To find the inverse function, f ⁻¹(x), of the function f(x) = 5x, we need to follow a few steps. First, we swap the f(x) with x to get x = 5y. Here, 'y' represents the 'f ⁻¹(x)' we are looking for. Next, we solve this equation for y, which would be y = x/5. Therefore, the inverse function f ⁻¹(x) is x/5.
The relationship between a function and its inverse is that they essentially 'undo' each other. When you apply f(x) and then f ⁻¹(x) to any number, you should end up with the original number you started with, which is the case with f(x) and f ⁻¹(x) here.
The correct answer is option Mathematics, High School. If f(x) = 5x, the inverse function f ⁻¹(x) is found by swapping the roles of x and f(x) in the equation. So, we have:
f(x) = 5x x = 5f⁻¹(x)
To solve for f⁻¹(x), we isolate f⁻¹(x) by dividing both sides of the equation by 5 to get:
f⁻¹(x) = x/5
Therefore, the inverse function of f(x) = 5x is f⁻¹(x) = x/5.