Which represents the inverse of the function f(x) = 4x? h(x) = x + 4, h(x) = x – 4, h(x) = 3/4 x, h(x) = 1/4 x
Answer: The inverse of the function f(x) = 4x is h(x) = 1/4 x.
Functions and Inverses
In mathematics, the inverse of a function reverses the operation of the original function. For the function f(x) = 4x, the inverse would undo the multiplication by 4, which is achieved by dividing by 4, represented as h(x) = 1/4 x. Understanding functions and their inverses is crucial in algebra and calculus, as it provides insights into the symmetrical relationship between operations and is fundamental in solving equations and modeling real-world phenomena.
FAQ on Functions and Inverses
What is the inverse of f(x) = x + 5?
The inverse is h(x) = x – 5.
What is the inverse of f(x) = x² (x > 0)?
The inverse is h(x) = √x.
What is the inverse of f(x) = 1/x?
The inverse is h(x) = 1/x.
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