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.

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