Question

range of f(x)=1/4-x^2​

Answer 1

$\boxed{ \tt{Question :}}$

$\tt \pink{→ Range \: of \: \: f(x)= \frac{1}{4}- {x}^{2}}$

$\boxed{\tt{Solution :}}$

$\tt{→ The \: Domain \: is \: x ∈ (-2 \: and \: 2)}$

$\tt{→ The \: range \: is \: \: \frac{1}{2} + \infty }$

$\boxed{ \tt{Explanation :}}$

$\tt \blue{→ The \: function \: is \: f(x) = \frac{1}{ \sqrt{4 - {x}^{2} } }}$

$\tt \blue{→ Therefore ,}$

$\tt \blue{→4 - {x}^{2}> 0}$

$\tt \blue{→ (2 - x) \: \: (2 + x) > 0}$

$\tt \blue{→ 2 - x > 0}$

$\tt \blue{→ 2 + x > 0}$

$\tt \blue{→ (x < 2)\: and \: (x > - 2)}$

Note :

Note :→ What'under the “√” sign must be ≥ 0 and we cannot divide by 0.