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Chapter 1: Problem 28

Evaluate each function at the given values of the independent variable and simplify. \(f(x)=3 x+7\) a. \(f(4)\) b. \(f(x+1)\) c. \(f(-x)\)

Short Answer

Expert verified
The evaluated function for given values results in: \(f(4)=19\), \(f(x+1)=3x+10\), and \(f(-x)=-3x+7\).

Step by step solution

01

Evaluate \(f(4)\)

To find the value of function at \(x=4\), substitute \(4\) in place of \(x\) in the function. It becomes \(f(4) = 3*4+7 = 12+7 = 19\). So, \(f(4) = 19\).
02

Evaluate \(f(x+1)\)

Now take \(x+1\) and substitute in place of \(x\) in the function. It results in\n\n\(f(x+1) = 3*(x+1)+7 = 3x+3+7 = 3x+10\).\n\nSo, \(f(x+1) = 3x+10\).
03

Evaluate \(f(-x)\)

Lastly, replace \(x\) in the function with \(-x\). It gives\n\n\(f(-x) = 3*(-x)+7 = -3x+7\). \n\nSo, \(f(-x) = -3x+7\).

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