Find the inverse of the function f(x)=√(x), for x ≥0 . Verify that f(f^-1(x))=x and f^-1(f(x))=x

step 1 So this problem first asks us to find the inverse of a given function. So we have the function f

Find the inverse of the function f(x)=√(x), for x ≥0 ....

Key Concepts

Verification of Inverse Functions

Verification of inverse functions is carried out by composing the function and its inverse and demonstrating that the composition in both orders returns the original input. This process confirms the correctness of the inverse function by showing that it appropriately reverses the effect of the original function.

Function Composition

Function composition involves applying one function to the result of another function. In terms of inverses, composing a function with its inverse (in either order) should yield the identity function, meaning the output will be the input. This property provides a method for verifying whether two functions are indeed inverses of each other.

Domain and Range

The domain of a function is the set of all valid inputs, while the range is the set of possible outputs. In the context of inverse functions, the domain of the original function becomes the range of its inverse, and vice versa. Paying attention to these sets is crucial, as determining the correct domain and range ensures the function and its inverse are properly defined.

Inverse Functions

Inverse functions are functions that 'undo' the action of the original function, meaning if you apply a function and then its inverse, you return to the starting value. Finding an inverse involves swapping the dependent and independent variables and then solving for the new dependent variable, which reflects the reversed relationship between inputs and outputs.

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