You will need

- - handle;
- paper

Instruction

1

Consider the scope

**of the definition**of some elementary functions. If the function has the form y = a/b a region**determination**are all values except zero. The number a is any number. For example, to find the region of**definition***of the function*y = 3/2x-1, it is necessary to find those values of x for which the denominator of the given fraction is not zero. To do this, find the values of x for which the denominator is equal to zero. For this Paranaita the denominator to zero and find the value, solving the resulting equation for x : 2x – 1 = 0; 2x = 1; x = ½; x = 0,5. It follows that the**definition***of the function*will be any number other than 0.5 in.2

To find the region of

**definition***of the function*radical expression with an even exponent, consider the fact that this expression must be greater than or equal to zero. Example: Find the area**of definition***of the function*y = √3x-9. Referring to the above condition, the expression takes the form of the inequality: 3x – 9 ≥ 0. Solve the following: 3x ≥ 9; x ≥ 3. So, the scope**of definition**of this*function*will be all values of x greater than or equal to 3, i.e., x ≥ 3.3

Finding the area

**of definition***of the function*radical expression with an odd exponent, you need to remember the rule that x can be any number if the radical expression is not a fraction. For example, to find the region of**definition***of the function*y = 3√2x-5 , it is sufficient to indicate that x is any real number.4

While the field

**definition**logarithmic*functions*, remember that the expression standing under the sign of the logarithm must be a positive value. For example, find the area**of definition***of the function*y = log2 (4x – 1). Given the above condition, find the area**of definition***of the function*in the following way: 4x – 1 > 0; hence 4 > 1; x > 0,25. Thus, the scope**of the definition***of the function*y = log2 (4x – 1) are all values of x > 0,25.