Problem 28

Question

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. \(f(-x)\)

Step-by-Step Solution

Verified
Answer
The evaluated function for given values results in: \(f(4)=19\), \(f(x+1)=3x+10\), and \(f(-x)=-3x+7\).
1Step 1: 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, \(f(4) = 19\).
2Step 2: 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, \(f(x+1) = 3x+10\).
3Step 3: Evaluate \(f(-x)\)
Lastly, replace \(x\) in the function with \(-x\). It gives\n\n\(f(-x) = 3*(-x)+7 = -3x+7\). \n\nSo, \(f(-x) = -3x+7\).