If-x≤x≤-2x then find the interval in which x lies.
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Brainly.in
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If -2 < x ≤ 3 then find the interval in which 2-3x lies.
Answer · 3 votes
it is given that -2 < x ≤ 3 then we have to find the interval in which 2 - 3x lies -2 < x ≤ 3 when we change sign of x, sign of inequality change as shown below. a ≤ x ≤ b ⇒-a ≥ -x ≥ - b so, -2 < x ≤ 3 ⇒-(-2) > -x ≥ -3 ⇒2 > -x ≥ -3 ⇒-3 ≤ -x < 2 ⇒ -3 × 3 ≤ -3x < 3 × 2⇒-9 ≤ -3x < 6⇒2 - 9 ≤ 2 - 3x < 2 + 6 ⇒-7 ≤ 2 - 3x < 8 therefore, [-7, 8) is the interval in which 2 - 3x lies.
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Toppr
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If x is real then the function f(x) = (x^2-2x+4x^2+2x+4) lies in the interval
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Given: y = x^2-2x+4x^2+2x+4 Discriminant of x^2 - 2x + 4 is Δ = ( - 2 )^2 - 4 × 1 × 4 = 4 - 16 = - 12<0 x∈ R Discriminant of x^2 + 2x + 4 is Δ = 2^2 - 4 × 1 × 4 = 4 - 16 = - 12<0 x∈ R y (x^2 + 2x + 4 ) = x^2 - 2x + 4 (y - 1 )x^2 + 2 (y + 1 )x + 4 (y - 1 ) = 0 is quadratic in x for all x∈ R Δ> 0 4 (y + 1 )^2 - 4 × (y - 1 )4 (y - 1 )> 0 (y + 1 )^2 - (2y - 2 )^2> 0 (y + 1 + 2y - 2 ) (y + 1 - 2y + 2 )> 0 (3y - 1 ) ( - y + 3 )> 0 (3y - 1 ) (y - 3 )< 0 y∈ [ 13,3 ]
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