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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.
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.
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.
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.