Question 37
Given functions $f$ and $g$, determine the domain of $f+g$.
\[
f(x)=3 x-4, \quad g(x)=5 x+3
\]
$(-$
(A),-3$)$ or $(-3$
)
(0)
(8)
(C)
$0)$ or $(0$
)
$(-$
(D)
$\infty$
)

Answer

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Answer

$\boxed{(-\infty, \infty)}$

Steps

Step 1 ：Given functions $f(x)=3x-4$ and $g(x)=5x+3$

Step 2 ：To find the domain of $f+g$, we need to find the intersection of their individual domains.

Step 3 ：Since both functions are linear, their domains are all real numbers.

Step 4 ：Thus, the domain of $f+g$ is also all real numbers.

Step 5 ：$\boxed{(-\infty, \infty)}$