Questions: Suppose f(x)=15x-3. f(z-4)+f(4z)=

Suppose f(x)=15x-3. f(z-4)+f(4z)=
Transcript text: Suppose $f(x)=15 x-3$. \[ f(z-4)+f(4 z)= \]
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Solution

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Solution Steps

Solution Approach
  1. First, we need to evaluate \( f(z-4) \) by substituting \( z-4 \) into the function \( f(x) = 15x - 3 \).
  2. Next, we need to evaluate \( f(4z) \) by substituting \( 4z \) into the function \( f(x) = 15x - 3 \).
  3. Finally, we add the results of \( f(z-4) \) and \( f(4z) \) together.
Step 1: Evaluate \( f(z-4) \)

We start by substituting \( z-4 \) into the function \( f(x) = 15x - 3 \): \[ f(z-4) = 15(z-4) - 3 = 15z - 60 - 3 = 15z - 63 \]

Step 2: Evaluate \( f(4z) \)

Next, we substitute \( 4z \) into the function: \[ f(4z) = 15(4z) - 3 = 60z - 3 \]

Step 3: Add the Results

Now, we add the two results together: \[ f(z-4) + f(4z) = (15z - 63) + (60z - 3) = 75z - 66 \]

Step 4: Substitute \( z = 5 \)

Finally, we substitute \( z = 5 \) into the expression: \[ 75(5) - 66 = 375 - 66 = 309 \]

Final Answer

\(\boxed{309}\)

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