Find-the-range-of-f-x-3-2-x-2-

Question Number 16457 by Tinkutara last updated on 22/Jun/17

Find the range of f (x) = \frac{3}{2 - x^{2}}

Answered by sandy_suhendra last updated on 22/Jun/17

y = \frac{3}{2 - x^{2}}

y (2 - x^{2}) = 3

2 y - x^{2} y = 3

x^{2} y = 2 y - 3

x^{2} = \frac{2 y - 3}{y}

x = \sqrt{\frac{2 y - 3}{y}}

f^{- 1} (x) = \sqrt{\frac{2 x - 3}{x}}

range of f (x) is domain of f^{- 1} (x)

\frac{2 x - 3}{x} ⩾ 0 \Rightarrow x < 0 or x ⩾ 1 \frac{1}{2}

range of f (x) = {y ∣ y < 0 or y ⩾ 1 \frac{1}{2}}