if-f-x-2-x-show-that-f-x-3-f-x-1-15-2-f-x-

Question Number 23922 by chernoaguero@gmail.com last updated on 09/Nov/17

if f (x) = 2^{x}

show that f (x + 3) - f (x - 1) = \frac{15}{2} f (x)

Answered by $@ty@m last updated on 10/Nov/17

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

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

∴ L H S = f (x + 3) - f (x - 1)

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

= \frac{15}{2} f (x) = R H S

Commented by chernoaguero@gmail.com last updated on 10/Nov/17

Thank u sir God bless u