Find the domain and range of function f(x) = \(x-2\over 3-x\).

Solution :

we have,  f(x) = \(x-2\over 3-x\)

Domain of f : Clearly f(x) is defined for all x satisfying 3 – x \(\ne\) 0 i.e. x \(\ne\) 3

Hence, Domain of f is R – {3}

Range of f : Let y = f(x), i.e.  y = \(x-2\over 3-x\)

\(\implies\) 3y – xy = x – 2

= x(y + 1) = 3y + 2

\(\implies\) x = \(3y + 2\over y + 1\)

Clearly, x assumes real values for all y expect y + 1 = 0 i.e. y = -1

Hence, Range of f is R – {-1}


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