Use the piecewise-defined function to find the fol

Questions: Use the piecewise-defined function to find the following values for (f(x)). (f(x)=leftbeginarrayll 1-3 x text if x leq 1 3 x text if 1<x<7 4 x+3 text if x geq 7 endarrayright.) Find (f(-1), f(1), f(4), f(6)), and (f(7)).

Transcript text: Use the piecewise-defined function to find the following values for $f(x)$. \[ f(x)=\left\{\begin{array}{ll} 1-3 x & \text { if } x \leq 1 \\ 3 x & \text { if } 1

Solution

Solution Steps

To find the values of the piecewise-defined function $ f(x) $ at specific points, we need to determine which piece of the function applies to each given value of $ x $. We then substitute the value of $ x $ into the appropriate expression to calculate $ f(x) $.

For $ f(-1) $, since $ -1 \leq 1 $, use the first piece: $ f(x) = 1 - 3x $.
For $ f(1) $, since $ 1 \leq 1 $, use the first piece: $ f(x) = 1 - 3x $.
For $ f(4) $, since $ 1 < 4 < 7 $, use the second piece: $ f(x) = 3x $.
For $ f(6) $, since $ 1 < 6 < 7 $, use the second piece: $ f(x) = 3x $.
For $ f(7) $, since $ 7 \geq 7 $, use the third piece: $ f(x) = 4x + 3 $.

Step 1: Calculate $ f(-1) $

For $ x = -1 $, since $ -1 \leq 1 $, we use the first piece of the function: \[ f(-1) = 1 - 3(-1) = 1 + 3 = 4 \]

Step 2: Calculate $ f(1) $

For $ x = 1 $, since $ 1 \leq 1 $, we again use the first piece of the function: \[ f(1) = 1 - 3(1) = 1 - 3 = -2 \]

Step 3: Calculate $ f(4) $

For $ x = 4 $, since $ 1 < 4 < 7 $, we use the second piece of the function: \[ f(4) = 3(4) = 12 \]

Step 4: Calculate $ f(6) $

For $ x = 6 $, since $ 1 < 6 < 7 $, we again use the second piece of the function: \[ f(6) = 3(6) = 18 \]

Step 5: Calculate $ f(7) $

For $ x = 7 $, since $ 7 \geq 7 $, we use the third piece of the function: \[ f(7) = 4(7) + 3 = 28 + 3 = 31 \]

Final Answer

The values of the function at the specified points are:

$ f(-1) = 4 $
$ f(1) = -2 $
$ f(4) = 12 $
$ f(6) = 18 $
$ f(7) = 31 $

Thus, the final answers are: \[ \boxed{f(-1) = 4} \] \[ \boxed{f(1) = -2} \] \[ \boxed{f(4) = 12} \] \[ \boxed{f(6) = 18} \] \[ \boxed{f(7) = 31} \]

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Questions: Use the piecewise-defined function to find the following values for (f(x)). (f(x)=leftbeginarrayll 1-3 x text if x leq 1 3 x text if 1<x<7 4 x+3 text if x geq 7 endarrayright.) Find (f(-1), f(1), f(4), f(6)), and (f(7)).

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Solution Steps

Final Answer

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