Analyzing the Rational Function: Determine the Domain of (5-x)/(2-x)

Question

Given the following function:

5x2x \frac{5-x}{2-x}

Does the function have a domain? If so, what is it?

Video Solution

Solution Steps

00:00 Does the function have a domain? And if so, what is it?
00:04 To find the domain, remember that division by 0 is not allowed
00:08 Therefore, let's see what solution zeroes the denominator
00:10 Let's isolate X
00:17 And this is the solution to the question

Step-by-Step Solution

To determine the domain of the function 5x2x \frac{5-x}{2-x} , we need to identify and exclude any values of x x that make the function undefined. This occurs when the denominator equals zero.

  • Step 1: Set the denominator equal to zero:
    2x=0 2-x = 0
  • Step 2: Solve for x x :
    Adding x x to both sides gives 2=x 2 = x . Hence, x=2 x = 2 .

This means that the function is undefined when x=2 x = 2 . Therefore, the domain of the function consists of all real numbers except x=2 x = 2 .

Thus, the domain is: x2 x \ne 2 .

The correct answer choice is:

Yes, x2 x\ne2

Answer

Yes, x2 x\ne2