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Question
Write the domain and range of the function \[f\left( x \right) = \frac{x - 2}{2 - x}\] .
Solution
Given: \[f\left( x \right) = \frac{x - 2}{2 - x}\] Domain ( f ) :
Clearly, f (x) is defined for all x satisfying: if 2 -x ≠ 0 ⇒ x ≠ 2.
Hence, domain ( f ) = R -{2}
Range of f :
Let f (x) = y
⇒ \[\frac{x - 2}{2 - x} = y\]
⇒ x - 2 = y (2 -x)
⇒ x -2 = - y (x -2)
⇒ y = -1
Hence, range ( f ) = { -1}.
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