Instruction

1

Find

**the area****definition**is the first thing to do when working with functions. This set of numbers, which belongs to the argument*of the function*, with the imposition of certain restrictions arising from the use of it in terms of certain mathematical structures, for example, square root, fractions, logarithms, etc.2

As a rule, all these structures can be attributed to six main types and their various combinations. Need to solve one or more of the inequalities to determine the points at which a function cannot exist.

3

The power function with the exponent as a fraction with an even, znamenatelnih a function of the form u^(m/n). Obviously, radical expression cannot be negative, therefore, we need to solve the inequality u≥0.Example 1: y=√(2•x - 10).Solution: write the inequality 2•x – 10 ≥ 0 → x ≥ 5. Scope

**definition**is the interval [5; +∞). When x4

Logarithmic function of the form log_a (u)In this case, the inequality is strict, u>0, since the expression under the sign of the logarithm cannot be less than zero.Example 2: y=log_3 (x - 9).Solution: x – 9 > 0 → x > 9 → (9; +∞).

5

Fraction of the form u(x)/v(x)Obviously, the denominator cannot go to zero so critical points can be found from the equality v(x) = 0.Example 3: y = 3•x2 – 3/(X3 + 8).Solution: X3 + 8 = 0 → X3 = -8 → x=-2 → (-∞; -2)U(-2; +∞).

6

Trigonometric

*functions*tg and ctg u inaudita constraints from the inequality x ≠ π/2 + π•k.Example 4: y = tg (x/2).Solution: x/2 ≠ π/2 + π•k → x ≠ π•(1 + 2•k).7

Trigonometric

*functions*arcsin u and asso onesite bilateral inequality -1 ≤ u ≤ 1.Example 5: y = 4 arcsin•x. Solution: -1 ≤ 4•x ≤ 1 → -1/4 ≤ x ≤ 1/4.8

The exponential-power

*function*of the form u(x)^v(x)Region**definition**is the restriction to u>0.Example 6: y = (X3 + 125)^p.Solution: X3 + 125 >0 → x > -5 → (-5; +∞).9

The presence of

*functions*of two or more of the above expressions imply the imposition of more stringent restrictions, taking into account all the components. You need to find them separately, and then combined into a single interval.