Question

What is the range of f(x) = $\frac{x^2-5x+6}{(x-3)}$ ( R $\to$ set of all real numbers )

• A. R
• B. R-{1}
• C. R-{3)
• D. R-{2}

Answer 1

The correct option is B

R-{1}

f(x) = $\frac{(x-3)(x-2)}{(x-3)}$

= x -2 , if x $\ne$ 3

One important thing to note here is that $\frac{x^2-5x+6}{(x-3)}$ are not the same functions,

They are same at all points except at x = 3. They behae the same way when x $\ne$ 3.

Range of x - 2 is R.

f(x) is not defined at x = 3 , so the range will be R - { f(3) } = R - {1}.