First slide

Functions (XII)

Question

$Number of integral values of x satisfying the inequality {(\frac{3}{4})}^{6 x + 10 - x^{2}} < \frac{27}{64} is$

Moderate

Solution

${(\frac{3}{4})}^{6 x + 10 - x^{2}} < {(\frac{3}{4})}^{3} \Rightarrow 6 x + 10 - x^{2} > 3 x^{2} - 6 x - 7 < 0 \Rightarrow (x - 7) (x + 1) < 0 \Rightarrow - 1 < x < 7$

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