Find the Domain of the Sum of the Functions f(x)=4x , g(x)=3x+1

$f (x) = 4 x$ , $g (x) = 3 x + 1$

Step 1

Find the sum of the functions.

Replace the function designators with the actual functions in $f (x) + g (x)$ .

$4 x + 3 x + 1$

Add $4 x$ and $3 x$ .

$7 x + 1$

Step 2

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 3

Find the Domain of the Sum of the Functions f(x)=4x , g(x)=3x+1

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