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The image contains a mathematical problem involving the function \( f(x) = \frac{5}{2x-9} \). It asks for the domain of this function.

To find the domain of \( f(x) \), we need to determine where the function is defined. The function is undefined where the denominator is zero, so we set the denominator equal to zero and solve for \( x \):

\[ 2x - 9 = 0 \]
\[ 2x = 9 \]
\[ x = \frac{9}{2} \]

Therefore, \( f(x) \) is undefined at \( x = \frac{9}{2} \). The domain of \( f(x) \) is all real numbers except \( x = \frac{9}{2} \). In interval notation, this is:

\[ \text{Domain of } f(x): (-\infty, \frac{9}{2}) \cup (\frac{9}{2}, \infty) \]

Would you like more details or have any other questions on this topic?

1. How do you determine the range of the function \( f(x) = \frac{5}{2x-9} \)?
2. What happens to the function as \( x \) approaches \( \frac{9}{2} \) from the left and from the right?
3. How would the graph of this function look?
4. Can you explain the concept of vertical asymptotes in relation to this function?
5. How would the function change if the numerator was a variable term instead of a constant?

**Tip:** When finding the domain of rational functions, always check for values that make the denominator zero, as these are excluded from the domain.

Diketahui fungsi f(x) = 5/(2x-9). Daerah asal fungsi f(x) adalah ...

This example explains how to find the domain of the rational function f(x) = 5/(2x-9). Learn how to exclude values that make the denominator zero. Suitable for high school students studying algebra.

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