f(x)=2^x হলে f (x+3)-f (x-1)=?

দেওয়া আছে, \(f(x) = 2^x\)

সুতরাং,

\(f(x+3) = 2^{x+3} = 2^x \cdot 2^3 = 8 \cdot 2^x\)

\(f(x-1) = 2^{x-1} = \frac{2^x}{2} = \frac{1}{2} \cdot 2^x\)

অতএব,

\(f(x+3) - f(x-1) = 8 \cdot 2^x - \frac{1}{2} \cdot 2^x\)

\(= 2^x \left(8 - \frac{1}{2}\right)\)

\(= 2^x \left(\frac{16 - 1}{2}\right)\)

\(= 2^x \cdot \frac{15}{2}\)

\(= \frac{15}{2} \cdot 2^x\)

\(= \frac{15}{2} f(x)\) 🎉