The domain of the given function is required.
The domain is (-∞,3/2),(3/2,∞)
Domain of a function
The given function is [tex]f(x)=\dfrac{x-5}{2x-3}[/tex]
The domain of a function are the values of x for which the given function is defined.
The function is undefined when [tex]x=\dfrac{3}{2}[/tex]
[tex]f(3/2)=\dfrac{\dfrac{3}{2}-5}{2\times \dfrac{3}{2}-3}=\infty[/tex]
So, [tex]x\neq \dfrac{3}{2}[/tex]
The domain is [tex]\left(-\infty,\dfrac{3}{2}\right),\left(\dfrac{3}{2},\infty\right)[/tex]
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