Question

The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is ______.

Options

• R - {- 5}

• R - {- 1}

• R - {1}

• R - {5}

Answer 1

The range of the function f(x) = `(x - 3)/(5 - x)`, x ≠ 5 is R - {- 1}.

Explanation:

We have, f(x) = `(x - 3)/(5 - x)`

Put, f(x) = y

∴ y = `(x - 3)/(5 - x)`

⇒ 5y - xy = x - 3

x(y + 1) = 5y + 3

x = `(5x + 3)/(y + 1)`

∴ y ∈ R - {- 1}

∴ Range of f(x) = R - {- 1}