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❓ Question Let y = [ x ] y=[x] be the Greatest Integer Function (GIF), and y = { x } y=\{x\} be the Fractional Part Function. The graph of y = …

❓ Question Given f ( x ) = log ⁡ ( 1 + x 1 − x ) , f(x)=\log\left(\frac{1+x}{1-x}\right), find f ( 3 x + x 3 1 + 3 x 2 ) . f\left(\frac{3x+x^3}{…

❓ Question If u + log ⁡ 4 3 u + log ⁡ 2 3 = u + log ⁡ 8 3 u + log ⁡ 4 3 = V , \frac{u+\log_{4}3}{u+\log_{2}3} = \frac{u+\log_{8}3}{u+\log_{4}3} =…

❓ Question Given that x > 13 , x>13, solve log ⁡ x − 1 1 ⋅ log ⁡ x − 2 ( x − 1 ) ⋅ log ⁡ x − 3 ( x − 2 ) ⋯ log ⁡ x − 12 ( x − 11 ) = 2. \l…

❓ Question Given 2 x + y = 6 y , 3 x − 1 = 2 y + 1 , 2^{x+y}=6^y,\qquad 3^{x-1}=2^{y+1}, where x = x 1 , y = x 2 . x=x_1,\qquad y=x_2. Find log…

❓ Question Find the number of solutions of ∣ 2 x − 1 ∣ + ∣ 4 − 2 x ∣ < 3. |2^x-1|+|4-2^x|<3. ✍️ Solution Let t = 2 x ( t > 0 ) . t=2^…

❓ Question If f ( x ) = x 2 + 2 x + 1 − x 2 − 2 x + 1 , f(x)=\sqrt{x^2+2x+1}-\sqrt{x^2-2x+1}, find f ⁣ ( − 5 4 ) + f ⁣ ( 3 4 ) + f ⁣ ( 7 4 ) …