Answered

Join the conversation on IDNLearn.com and get the answers you seek from experts. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.

Select the correct answer.

The domain, range, and [tex]\( x \)[/tex]-intercept of a one-to-one function are shown.

\begin{tabular}{|l|l|c|}
\hline \multicolumn{1}{|c|}{domain:} & \multicolumn{1}{|c|}{range:} & [tex]\( x \)[/tex]-intercept: \\
\hline
[tex]\( x \geq 2 \)[/tex] & [tex]\( y \geq -3 \)[/tex] & [tex]\((11, 0)\)[/tex] \\
\hline
\end{tabular}

Which set of information could be characteristics of the function's inverse?

A. domain: [tex]\( x \geq -3 \)[/tex]; range: [tex]\( y \geq 2 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\((0, 11)\)[/tex]

B. domain: [tex]\( x \geq 3 \)[/tex]; range: [tex]\( y \geq -2 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\((0, 11)\)[/tex]

C. domain: [tex]\( x \geq -2 \)[/tex]; range: [tex]\( y \geq 3 \)[/tex]; [tex]\( x \)[/tex]-intercept: [tex]\((-11, 0)\)[/tex]

D. domain: [tex]\( x \geq 2 \)[/tex]; range: [tex]\( y \geq -3 \)[/tex]; [tex]\( x \)[/tex]-intercept: [tex]\((-11, 0)\)[/tex]

Sagot :

GinnyAnsweridn
To determine the characteristics of the inverse function, we need to understand the relationships between the domain, range, and intercepts of a function and its inverse.

1. Domain and Range:
- The domain of the original function becomes the range of the inverse function.
- The range of the original function becomes the domain of the inverse function.

2. Intercepts:
- The [tex]$x$[/tex]-intercept of the original function becomes the [tex]$y$[/tex]-intercept of the inverse function, because the inverse function swaps the roles of [tex]$x$[/tex] and [tex]$y$[/tex].

Given:
- The domain of the function is [tex]\( x \geq 2 \)[/tex].
- The range of the function is [tex]\( y \geq -3 \)[/tex].
- The [tex]\( x \)[/tex]-intercept of the original function is [tex]\((11, 0)\)[/tex].

Now let's find the corresponding characteristics of the inverse function:

1. Domain of the Inverse Function: Since the range of the original function is [tex]\( y \geq -3 \)[/tex], this will become the domain of the inverse function. So the domain of the inverse function is [tex]\( x \geq -3 \)[/tex].

2. Range of the Inverse Function: Since the domain of the original function is [tex]\( x \geq 2 \)[/tex], this will become the range of the inverse function. So the range of the inverse function is [tex]\( y \geq 2 \)[/tex].

3. Intercept of the Inverse Function: The [tex]$x$[/tex]-intercept of the original function is [tex]\((11, 0)\)[/tex]. This point will be swapped to become the [tex]$y$[/tex]-intercept of the inverse function. Thus, the [tex]$y$[/tex]-intercept of the inverse function is [tex]\((0, 11)\)[/tex].

Summarizing the characteristics of the inverse function:
- Domain: [tex]\( x \geq -3 \)[/tex]
- Range: [tex]\( y \geq 2 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\((0, 11)\)[/tex]

Upon examining the given options, we see that Option A matches all these characteristics:
- Domain: [tex]\( x \geq -3 \)[/tex]
- Range: [tex]\( y \geq 2 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\((0, 11)\)[/tex]

Therefore, the correct answer is:

A. domain: [tex]$x \geq -3$[/tex]; range: [tex]$y \geq 2$[/tex]; y-intercept: [tex]$(0, 11)$[/tex]
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Find the answers you need at IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.