Question

given f(x) = x + 1 and g(x) = 3x - 1, evaluate each below. show all work for credit.

1. (f + g)(x)
2. (g - f)(x)
3. (f + g)(3)
4. (f - g)(2)

Explanation:

14. \((g - f)(x)\)

Step1: Recall the formula for subtraction of functions

The formula for \((g - f)(x)\) is \(g(x)-f(x)\).

Step2: Substitute the given functions

We know \(f(x)=x + 1\) and \(g(x)=3x-1\). So, \(g(x)-f(x)=(3x - 1)-(x + 1)\).

Step3: Simplify the expression

First, distribute the negative sign: \(3x-1 - x - 1\). Then, combine like terms: \((3x - x)+(-1 - 1)=2x-2\).

Step1: Recall the formula for addition of functions

We already found in problem 13 that \((f + g)(x)=4x\).

Step2: Substitute \(x = 3\) into \((f + g)(x)\)

Substitute \(x = 3\) into \(4x\), we get \(4\times3\).

Step3: Calculate the result

\(4\times3 = 12\).

Step1: Recall the formula for subtraction of functions

The formula for \((f - g)(x)\) is \(f(x)-g(x)\).

Step2: Substitute the given functions

We know \(f(x)=x + 1\) and \(g(x)=3x-1\). So, \(f(x)-g(x)=(x + 1)-(3x - 1)\).

Step3: Simplify the expression

First, distribute the negative sign: \(x + 1-3x + 1\). Then, combine like terms: \((x-3x)+(1 + 1)=-2x + 2\).

Step4: Substitute \(x = 2\) into the simplified function

Substitute \(x = 2\) into \(-2x + 2\), we get \(-2\times2+2\).

Step5: Calculate the result

\(-2\times2+2=-4 + 2=-2\).

Answer:

\(2x - 2\)

15. \((f + g)(3)\)