Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Ask your questions and receive precise answers from experienced professionals across different disciplines. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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]

Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.