Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Which represents the inverse of the function f(x) 4x?
O h(x) = x + 4
O h(x) = x - 4
O h(x) Sx
O h(x) = ~x

Sagot :

semsee45

Answer:

[tex]h(x)=\dfrac{1}{4}x[/tex]

Step-by-step explanation:

The inverse of a function is its reflection in the line y = x.

Given function:

[tex]f(x)=4x[/tex]

The given function has an unrestricted domain and range.

  • Domain:  (-∞, ∞)  →  all real numbers.
  • Range:  (-∞, ∞)  →  all real numbers.

To find the inverse of the given function, first replace f(x) with y:

[tex]\implies y=4x[/tex]

Rearrange the equation to isolate x:

[tex]\implies \dfrac{y}{4}=\dfrac{4x}{4}[/tex]

[tex]\implies \dfrac{1}{4}y=x[/tex]

[tex]\implies x=\dfrac{1}{4}y[/tex]

Swap the x for f⁻¹(x) and the y for x:

[tex]\implies f^{-1}(x)=\dfrac{1}{4}x[/tex]

This is the inverse of the given function.

The domain of the inverse function is the range of the function.

The range of the inverse function is the domain of the function.

Therefore, the domain and the range of the inverse function are unrestricted.

  • Domain:  (-∞, ∞)  →  all real numbers
  • Range:  (-∞, ∞)  →  all real numbers

Therefore, the function that represents the inverse of f(x) = 4x is:

[tex]\boxed{h(x)=\dfrac{1}{4}x}[/tex]

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.