Find the domain of the following functions a) y = 3x ^ 3-4x + 7 b) y = x + 3 / 2x-5

The scope is all the values ​​that the variable x can take.

a) y = 3x ^ 3 – 4x + 7 – in this equation there is no division by a variable, there is no extraction of the square root from a variable, so we can substitute any number for x.

Answer. D (y) = (- ∞; + ∞).

b) y = (x + 3) / (2x – 5) – here we can substitute any number in the numerator instead of x, but not in the denominator; a fractional bar is a division, and you cannot divide by 0, so the expression in the denominator should not equal 0;

2x – 5 ≠ 0;

2x ≠ 5;

x ≠ 5: 2;

x ≠ 2.5 – only the number 2.5 cannot equal x, all other values ​​can be substituted.

Answer. D (y) = (- ∞; 2.5) ∪ (2.5; + ∞).