Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Join our Q&A platform and connect with professionals ready to provide precise answers to your questions in various areas. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

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 :

GinnyAnswer
To solve this problem, let's analyze the properties and characteristics of a one-to-one 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, say [tex]\((a, 0)\)[/tex], becomes the [tex]\( y \)[/tex]-intercept of the inverse function, which will be [tex]\((0, a)\)[/tex].

Given the original function:
- Domain: [tex]\( x \geq 2 \)[/tex]
- Range: [tex]\( y \geq -3 \)[/tex]
- [tex]\( x \)[/tex]-intercept: [tex]\( (11, 0) \)[/tex]

Let's find the corresponding properties for the inverse function:
- Domain of the inverse function: This will be the range of the original function, so we have [tex]\( x \geq -3 \)[/tex].
- Range of the inverse function: This will be the domain of the original function, so we have [tex]\( y \geq 2 \)[/tex].
- [tex]\( y \)[/tex]-intercept: The [tex]\( x \)[/tex]-intercept [tex]\( (11, 0) \)[/tex] of the original function becomes the [tex]\( y \)[/tex]-intercept of the inverse function, so we have [tex]\( (0, 11) \)[/tex].

Now, let's match these properties with the given answer choices:

A. Domain: [tex]\( x \geq -3 \)[/tex]; Range: [tex]\( y \geq 2 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\( (0, 11) \)[/tex]
This matches our calculated properties for the inverse function.

B. Domain: [tex]\( x \geq 3 \)[/tex]; Range: [tex]\( y \geq -2 \)[/tex]; [tex]\( y \)[/tex]-intercept: [tex]\( (0, 11) \)[/tex]
This does not match our calculated properties.

C. Domain: [tex]\( x \geq -2 \)[/tex]; Range: [tex]\( y \geq 3 \)[/tex]; [tex]\( x \)[/tex]-intercept: [tex]\( (-11, 0) \)[/tex]
This does not match our calculated properties.

D. Domain: [tex]\( x \geq 2 \)[/tex]; Range: [tex]\( y \geq -3 \)[/tex]; [tex]\( x \)[/tex]-intercept: [tex]\( (-11, 0) \)[/tex]
This does not match our calculated properties.

Therefore, the correct answer is:

[tex]\[ \boxed{A} \][/tex]

The inverse function's characteristics are:
- Domain: [tex]\( x \geq -3 \)[/tex]
- Range: [tex]\( y \geq 2 \)[/tex]
- [tex]\( y \)[/tex]-intercept: [tex]\( (0, 11) \)[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.