Questions: Answer the following for the function f(x)=(x-7)/(x+3). Be sure to show the steps for solving all parts of the problem on your scratchwork in order to receive full credit. Write each answer as an integer or reduced fraction. No decimal numbers, please. 1) Evaluate f(0) 2) Find z so that f(z)=3

Answer the following for the function f(x)=(x-7)/(x+3). Be sure to show the steps for solving all parts of the problem on your scratchwork in order to receive full credit. Write each answer as an integer or reduced fraction. No decimal numbers, please. 1) Evaluate f(0) 2) Find z so that f(z)=3
Transcript text: Part 1 of 2 Answer the following for the function $f(x)=\frac{x-7}{x+3}$. Be sure to show the steps for solving all parts of the problem on your scratchwork in order to receive full credit. Write each answer as an integer or reduced fraction. No decimal numbers, please. 1) Evaluate $f(0)$ Part 2 of 2 2) Find $z$ so that $f(z)=3$
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Solution

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Solution Steps

Step 1: Evaluate f(0)

Substitute \(x = 0\) into the function \(f(x) = \frac{x-7}{x+3}\): \(f(0) = \frac{0-7}{0+3} = \frac{-7}{3} = -\frac{7}{3}\)

Step 2: Find z so that f(z) = 3

Set \(f(z) = 3\): \(\frac{z-7}{z+3} = 3\)

Multiply both sides by \((z+3)\): \(z-7 = 3(z+3)\)

Distribute the 3 on the right side: \(z-7 = 3z+9\)

Subtract \(z\) from both sides: \(-7 = 2z+9\)

Subtract 9 from both sides: \(-16 = 2z\)

Divide both sides by 2: \(z = -8\)

Final Answer

  1. \(f(0) = -\frac{7}{3}\)
  2. \(z = -8\)
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