The domain of the function f x -9 x -27 2-3 x -2-219-32 x -1-1-4A- -3- -5-2- -C- -3-3-D- -0-1-

The correct option is B We must have 9^x + 27^ 2/3(x 2) 219 3 ^2(x 1)≥ 0 (3^x)^2 + 3 ^2(x 2) 219 3^2x 2≥ 0 (3^2x)+3^2x/81 219 3^2x/9≥ 0 ( 1 + 1/81 ...

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Byju's Answer

Standard XI

Mathematics

Sum of Infinite Terms of a GP

The domain of...

Question

$T h e d o m a i n o f t h e f u n c t i o n f (x) = {[9^{x} + 27^{\frac{2}{3} (x - 2)} - 219 - 3^{2 (x - 1)}]}^{\frac{1}{4}}$

[-3,3]

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[0,1]

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Solution

The correct option is C
$W e m u s t h a v e 9^{x} + 27^{\frac{2}{3} (x - 2)} - 219 - 3^{2 (x - 1)} \geq 0 (3^{x})^{2} + 3^{2 (x - 2)} - 219 - 3^{2 x - 2} \geq 0 (3^{2 x}) + \frac{3^{2 x}}{81} - 219 - \frac{3^{2 x}}{9} \geq 0 (1 + \frac{1}{81} - \frac{1}{9}) 3^{2 x} \geq 219 \frac{79}{81} \times 3^{2 x} \geq 219 3^{2 x} \geq 3 \times 81 = 3^{5} 2 x \geq 5 x \geq \frac{5}{2} \Rightarrow D o m a i n i s [\frac{5}{2}, \infty)$

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Similar questions

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The domain of the function f(x)=[9x+2723(x−2)−219−32(x−1)]14

The correct option is C We must have9x+2723(x−2)−219−32(x−1)≥0(3x)2+32(x−2)−219−32x−2≥0(32x)+32x81−219−32x9≥0(1+181−19)32x ≥2197981×32x≥21932x≥3×81=352x≥5x≥52⇒ Domain is [52,∞)

$T h e d o m a i n o f t h e f u n c t i o n f (x) = {[9^{x} + 27^{\frac{2}{3} (x - 2)} - 219 - 3^{2 (x - 1)}]}^{\frac{1}{4}}$