Evaluate this function at x=7. Write the exact answer. Do not round. If the answer is undefined, write Und as your answer. F(7)= This is a piecewise-defined function, represented as follows:\[ f(x) = \begin{cases} \frac{-6}{x+3} & \text{if } x \leq -5 \\ 3 & \text{if } -5 < x < 5 \\ 3^{-x+6} & \text{if } x \geq 5 \end{cases} \]The function $ f(x) $ is defined by three different expressions, each corresponding to a specific interval of the variable $ x $:1. For $ x \leq -5 $, the function is given by $ \frac{-6}{x+3} $.2. For values of $ x $ between $-5$ and $5$, the function equals $3$.3. For $ x \geq 5 $, the function is determined by the expression $3^{-x+6}$.

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Answered: f(x) = = -6 x + 3 3 3-x+6 if x < -5 if…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

Evaluate this function at x=7. Write the exact answer. Do not round. If the answer is undefined, write Und as your answer.

F(7)=

This is a piecewise-defined function, represented as follows:

\[
f(x) =
\begin{cases}
\frac{-6}{x+3} & \text{if } x \leq -5 \\
3 & \text{if } -5 < x < 5 \\
3^{-x+6} & \text{if } x \geq 5
\end{cases}
\]

The function $ f(x) $ is defined by three different expressions, each corresponding to a specific interval of the variable $ x $:

1. For $ x \leq -5 $, the function is given by $ \frac{-6}{x+3} $.
2. For values of $ x $ between $-5$ and $5$, the function equals $3$.
3. For $ x \geq 5 $, the function is determined by the expression $3^{-x+6}$.

Expert Solution

Step 1: Given

$T h e space g i v e n space p i e c e w i s e space f u n c t i o n space i s space f left parenthesis x right parenthesis equals open curly brackets table row cell fraction numerator negative 6 over denominator x plus 3 end fraction end cell cell i f space x less or equal than negative 5 end cell row 3 cell i f space minus 5 less than x less than 5 end cell row cell 3 to the power of negative x plus 6 end exponent end cell cell i f space x greater or equal than 5 end cell end table close$