Question

Drag the tiles to the correct boxes to complete the pairs. Match the one-to-one functions with their inverse functions. f(x) = 2 - 17 3 f(x)= x - 10 Inverse Function f-¹(x) = 5x f-¹ (x) = 2/² f¹(x) = x + 10 ƒ−¹ (x) = 3(x+17) 2 Reset f(x) = 2x Next Function f(x) = ²​

Answer 1

The question pertains to finding inverse functions in mathematics by reversing the effect of the original function. Examples provided illustrate the process of determining inverse functions by swapping input and output values. Functions are only invertible if they are one-to-one, where each input has a unique output.

Step-by-step explanation:

The question involves understanding the concept of inverse functions in mathematics. An inverse function essentially reverses the effect of the original function.

To find the inverse of a function, you would swap the roles of the input and output of the function, which graphically results in reflecting the function across the line y=x. For example, if f(x) = x + 10, the inverse function f^-1(x) would be f^-1(x) = x - 10. To match the functions with their respective inverses, check if applying the inverse function to the output of the original function returns the initial input value.

We can use the given examples to determine the correct pairs. If we start with the given function f(x) = 2x, the inverse would be the function that when multiplied by 2 gives the original input x; thus, f^-1(x) = x/2. Similarly, for the function f(x) = x - 10, adding 10 to both sides would give us the input, making f^-1(x) = x + 10. It is important to understand that not all functions have inverses, but one-to-one functions — functions where each input maps to a unique output — always have inverse functions.