Question

what is the domain of the function fx = √4-x2
$4 - {x}^{2}$
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Answer 1

$\large\underline\blue{\bold{Given \:  Question :-  }}$

$\sf \:  What \: is \: the \: domain \: of \: f(x) = \sqrt{4 - {x}^{2} }$

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$\huge \orange{AηsωeR} ✍$

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$\bf \:  ⟼ f(x) = \sqrt{4 - {x}^{2} }$

For domain of f(x) to be defined,

$\sf \:  ⟼4 - {x}^{2} \geqslant 0$

$\sf \:  ⟼ - ( {x}^{2} - 4) \geqslant 0$

$\sf \:  ⟼ {x}^{2} - 4 \leqslant 0$

$\sf \:  ⟼(x - 2)(x + 2) \leqslant 0$

$\bf\implies \: - 2 \leqslant x \leqslant 2$

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Theory and concept :-

A quadratic inequality is an equation of second degree that uses an inequality sign instead of an equal sign.

The solutions to quadratic inequality always give the two roots. The nature of the roots may differ and can be determined by discriminant (b2 – 4ac).

The general forms of the quadratic inequalities are:

ax^2 + bx + c < 0

ax^2 + bx + c ≤ 0

ax^2 + bx + c > 0

ax^2 + bx + c ≥ 0

To solve a quadratic inequality, we also apply the same method as illustrated in the procedure below:

• Write the quadratic inequality in standard form: ax2 + bx + c where a, b and are coefficients and a ≠ 0

• Determine the roots of the inequality.

• Write the solution in inequality notation or interval notation. If the quadratic inequality is in the form: (x – a) (x – b) ≥ 0, then x ≤ a or x ≥ b. if a < b, and if it is in the form :(x – a) (x – b) ≤ 0, when a < b then a ≤ x ≤ b,

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