Determine the domain of the function f(x) = (2x3 + sin(x)) / |x-2| and select the correct option.

March 31, 2026Mathematics

ScanSolve AI Answer

March 31, 2026

Answer

the domain of definition is all real numbers except $x=2$

Step 1: Solve Question 1. The function is $f(x) = \frac{2x^3 + \sin(x)}{|x-2|}$ . For the function to be defined, the denominator cannot be zero. $|x-2| \neq 0$ $x-2 \neq 0$ $x \neq 2$ The numerator $2x^3 + \sin(x)$ is defined for all real numbers. Therefore, the domain of definition is all real numbers except $x=2$ . This can be written as $(-\infty, 2) \cup (2, +\infty)$ .

The correct option is D.

Step 2: Solve Question 2. The function is $

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

More Mathematics Questions

QSolve: (x/x+1) - (x+1/3x-1) = 1/4 QConcrete blocks of length 1425m were laid end to end along the four side of a rectangular lawn 28m l…QBy selling his cow at Sh. 34,000, Obula made a loss of 15%. At what price had he bought the cow?QGiven that matrix A is [7 4p / 5p 5p]. (i) find the value of p for which the determinant of A is -2.…QDenkyemkrom is 35 km from Seidukrom on a bearing of 050°. Kyekyekrom is 12 km from Seidukrom on a be…

See all Mathematics questions →

Still have questions?

Quick Answer

Solve Question 1. The function is f(x) = (2x^3 + (x))/(|x-2|).

Asked on March 31, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on March 31, 2026

Step 1: Solve Question 1. The function is f(x) = (2x^3 + (x))/(|x-2|). For the function to be defined, the denominator cannot be zero. |x-2| ≠ 0 x-2 ≠ 0 x ≠ 2 The numerator 2x^3 + (x) is defined for all real numbers. Therefore, the domain of definition is all real numbers except x=2. This can be written as (-, 2) (2, +). The correct option is D. Step 2: Solve Question 2. The function is $