Find the domain of the function: y = √2x + 7

We need to find the domain of the function with square root y = √2x + 7.
The function with square root is defined only for those values of “x” when the radical expression is non-negative. In our case, 2x + 7 ≥ 0.
We solve the resulting inequality using identical transformations.
2x ≥ – 7;
we divide both sides of the inequality by 2 while the inequality sign is preserved.
x ≥ -7/2;
x ≥ – 3 1/2;
x ≥ – 3.5.
The domain of the function will be the segment [-3.5; + infinity)
Answer: ODZ = x Є [-3.5; + infinity).