If f(x)=2^x, then f(x+2)-f(x-2)= ?

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Answer 1 · 2017-10-15T05:39:45

# f(x+2)-f(x-2)=15/4*2^x, or 15*2^(x-2).#

Given that, #f(x)=2^x.#

#:. f(x+2)=2^(x+2), and, f(x-2)=2^(x-2).#

#:. f(x+2)-f(x-2)=2^(x+2)-2^(x-2),#

#=2^x*2^2-2^x*2^-2,#

#=2^x(2^2-2^-2),#

#=2^x(4-1/2^2)=(4-1/4)2^x,#

# rArr f(x+2)-f(x-2)=15/4*2^x, or 15*2^-2*2^x=15*2^(x-2).#