If #f(2x+1)=x^2#, find #f(x-1)-f(x+1)#?

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Answer 1 · 2017-11-19T06:17:59

#f(x-1)-f(x+1)=-x+1#

As #f(2x+1)=x^2#, let #t=2x+1#.

Therefore #x=(t-1)/2# and we can write #f(2x+1)=x^2# as #f(t)=(t-1)^2/4#

Hence #f(x-1)-f(x+1)#

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

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

= #(x^2-4x+4-x^2)/4#

= #-x+1#