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Maths-

General

Easy

Question

Let $g left parenthesis x right parenthesis$ be a function defined on [−1, 1] If the area of the equilateral triangle with two of its vertices at $left parenthesis 00 right parenthesis$ and $left square bracket x comma blank g left parenthesis x right parenthesis right square bracket$ is $fraction numerator square root of 3 over denominator 4 end fraction$ , then the function $g left parenthesis x right parenthesis$ is

$g (x) = \pm \sqrt{1 - x^{2}}$
$g (x) = \sqrt{1 - x^{2}}$
$g (x) = - \sqrt{1 - x^{2}}$
$g (x) = \sqrt{1 + x^{2}}$

The correct answer is: $g left parenthesis x right parenthesis equals plus-or-minus square root of 1 minus x to the power of 2 end exponent end root$

Related Questions to study

The ratio in which the area bounded by the curves $y to the power of 2 end exponent equals x$ and $x to the power of 2 end exponent equals y i s$ divided by the Iine $x equals fraction numerator 1 over denominator 2 end fraction$ is

The ratio in which the area bounded by the curves $y to the power of 2 end exponent equals x$ and $x to the power of 2 end exponent equals y i s$ divided by the Iine $x equals fraction numerator 1 over denominator 2 end fraction$ is

The area bounded by the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ , line $x equals square root of 3 y$ and $x$ ‐axis Iying in the first quadrant is

The area bounded by the circle $x to the power of 2 end exponent plus y to the power of 2 end exponent equals 4$ , line $x equals square root of 3 y$ and $x$ ‐axis Iying in the first quadrant is

If a curve $y equals 0 square root of x plus b x$ passes through the point $left parenthesis 1 comma blank 2 right parenthesis$ and the area bounded by the curve, Iine $x equals 4$ and $x$ ‐axis is 8 $s q$ units, then

If a curve $y equals 0 square root of x plus b x$ passes through the point $left parenthesis 1 comma blank 2 right parenthesis$ and the area bounded by the curve, Iine $x equals 4$ and $x$ ‐axis is 8 $s q$ units, then

parallel

The point of the contact of the tangent to the parabola $y to the power of 2 end exponent equals 4 a x$ , which makes an angle of 60° with x-axis, is

The point of the contact of the tangent to the parabola $y to the power of 2 end exponent equals 4 a x$ , which makes an angle of 60° with x-axis, is

The equation of the directrix of the parabola $x to the power of 2 end exponent plus 8 y minus 2 x equals 7$ is

The equation of the directrix of the parabola $x to the power of 2 end exponent plus 8 y minus 2 x equals 7$ is

The area enclosed by the parabolas $y equals x to the power of 2 end exponent minus 1$ and $y equals 1 minus x to the power of 2 end exponent$ is

The area enclosed by the parabolas $y equals x to the power of 2 end exponent minus 1$ and $y equals 1 minus x to the power of 2 end exponent$ is

parallel

The area between the curve $y to the power of 2 end exponent equals 4 o x comma$ $x$ -axis and the ordinates $x equals 0$ and $x equals o$ is

The area between the curve $y to the power of 2 end exponent equals 4 o x comma$ $x$ -axis and the ordinates $x equals 0$ and $x equals o$ is

The area of the region bounded by $y equals vertical line x minus 1 vertical line$ and $y equals 1$ is

The area of the region bounded by $y equals vertical line x minus 1 vertical line$ and $y equals 1$ is

The area of the plane region bounded by the curves $x plus 2 y to the power of 2 end exponent equals 0$ and $x plus 3 y to the power of 2 end exponent equals 1$ is equal to

The area of the plane region bounded by the curves $x plus 2 y to the power of 2 end exponent equals 0$ and $x plus 3 y to the power of 2 end exponent equals 1$ is equal to

parallel

The area bounded by the axes of reference and normal to $y equals I o g subscript e end subscript x$ at the point $left parenthesis 1 comma blank 0 right parenthesis$ is

The area bounded by the axes of reference and normal to $y equals I o g subscript e end subscript x$ at the point $left parenthesis 1 comma blank 0 right parenthesis$ is

The area bounded by the curve $y to the power of 2 end exponent equals 9 x$ and the line $x equals 1 comma x equals 4$ and $y equals 0$ in the first quadrant is

The area bounded by the curve $y to the power of 2 end exponent equals 9 x$ and the line $x equals 1 comma x equals 4$ and $y equals 0$ in the first quadrant is

The focus of the parabola $left parenthesis y minus 2 right parenthesis to the power of 2 end exponent equals 20 left parenthesis x plus 3 right parenthesis text is end text$

The focus of the parabola $left parenthesis y minus 2 right parenthesis to the power of 2 end exponent equals 20 left parenthesis x plus 3 right parenthesis text is end text$

parallel

The equation of the locus of a point which moves so as to be at equal distances from the point (a, 0) and the y-axis is

The equation of the locus of a point which moves so as to be at equal distances from the point (a, 0) and the y-axis is

$text The curve end text 16 x to the power of 2 end exponent plus 8 x y plus y to the power of 2 end exponent minus 74 x minus 78 y plus 212 equals 0 text represents end text$

$text The curve end text 16 x to the power of 2 end exponent plus 8 x y plus y to the power of 2 end exponent minus 74 x minus 78 y plus 212 equals 0 text represents end text$

The axis of the parabola $x to the power of 2 end exponent minus 4 x minus 3 y plus 10 equals 0 text is end text$

The axis of the parabola $x to the power of 2 end exponent minus 4 x minus 3 y plus 10 equals 0 text is end text$

parallel

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