We read your photo as:

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

March 31, 2026Mathematics

ScanSolve AI Answer

Answer

D

Graph of f(x) = (2x³ + sin(x))/|x − 2|

Step-by-step solution

2 steps

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.
Solve Question 2.
The function is $

Was this helpful?

Try one yourself

A new problem that tests the same skill.

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question

More Mathematics Questions

QDetermine the domain of the function f(x) = (2x3 + sin(x)) / ln|x-1|.QFind the domain and range of the function f(x) = 3/(x−2).QLet the function have domain (−2, −1, 0, 1, 2, 3) and be defined by f(x) = x?QGiven functions: f(x) = 2x + 3 where x [−1, 2) and g(x) = x2. Determine g(sqrt(3)), f⁻¹(x), a if…QFind the domain of the following functions: 1. f(x) = x/(x2+4) 2. f(x) = sqrt(x−4) 3. f(x)…

Browse by topic:Trigonometry Pre-Calculus

See all Mathematics questions →

Got a syllabus? Photograph it and I'll tell you what's due and what's worth the most.