Questions: Quiz 1
Find the domain of the function.
g(x)=3x/(x^2-25)
A. x x>25
B. x x ≠ -5,5
C. all real numbers
D. x x ≠ 0
Transcript text: Quiz 1
Find the domain of the function.
\[
g(x)=\frac{3 x}{x^{2}-25}
\]
A. $\{x \mid x>25\}$
B. $\{x \mid x \neq-5,5\}$
C. all real numbers
D. $\{x \mid x \neq 0\}$
Solution
Solution Steps
To find the domain of the function g(x)=x2−253x, we need to determine the values of x for which the function is defined. The function is undefined where the denominator is zero. Therefore, we solve the equation x2−25=0 to find the values of x that make the denominator zero. These values will be excluded from the domain.
Step 1: Identify the Function's Denominator
The function given is g(x)=x2−253x. To find the domain, we need to identify where the function is undefined. This occurs when the denominator is zero.
Step 2: Solve for Denominator Equal to Zero
Set the denominator equal to zero and solve for x:
x2−25=0
This can be factored as:
(x−5)(x+5)=0
Solving these equations gives:
x=5andx=−5
Step 3: Determine the Domain
The function is undefined at x=5 and x=−5. Therefore, the domain of the function is all real numbers except x=5 and x=−5.