CBSE

MATHEMATICS · Multi-part · CBSE · Mathematics · Power Play · Power Play

Problem

Let

p(x)=4\left(\dfrac{1}{3}\right)^{x}

. (i) Find the exact value of

p\left(\dfrac{3}{2}\right)

. (ii) Compute

p(-2)

. (iii) Simplify the ratio

\dfrac{p(-2)}{p\left(\dfrac{3}{2}\right)}

and express your answer as a single power of

3

. (iv) Prove that for any real number

x

p(x+1)=\dfrac{1}{3}\,p(x)