Find the domain of the function x/square root of 2x+8

We can start with "All real number," then we eliminate certain value what would cause zero in denominator;

Here, we have denominator of √ (2x+8)

We need to exclude value of x from real number such that √ (2x+8) = 0 So solve for x here;

√ (2x+8) = 0

[√ (2x+8) ]² = 0²

2x+8 = 0

2x = - 8

x = - 4

So we cannot have x to be - 4, otherwise denominator would be zero.

So exclude - 4 from "All real number"

Now we have domain of (-∞, - 4) U (-4, ∞) or All real number; x ≠ - 4.