# 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}

### Similar Questions

If y = 2[x] + 3 & y = 3[x – 2] + 5, then find [x + y] where [.] denotes greatest integer function.

Find the domain of the function f(x) = $$1\over x + 2$$.

Find the period of the function f(x) = $$e^{x-[x]+|cos\pi x|+|cos2\pi x|+ ….. + |cosn\pi x|}$$

Find the inverse of the function f(x) = $$log_a(x + \sqrt{(x^2+1)})$$; a > 1 and assuming it to be an onto function.

Find the range of the function $$log_{\sqrt{2}}(2-log_2(16sin^2x+1))$$