How can i prove that #h(x)=f(x-5)# when i know that #f(x-3)=g(3x-2)# , #g(3x+1)=h(x+3)# ??

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Answer 1 · 2017-05-31T09:46:39

See proof below

In the first equation

#f(x-3)=g(3x-2)#

Replace #x# by #(x+3)#

#f(x+3-3)=g(3(x+3)-2)#

#f(x)=g(3x+9-2)=g(3x+7)#

#f(x)=g(3x+7)#...........#(1)#

In the second equation,

#g(3x+1)=h(x+3)#

Replace #x# by #(x+2)#

#g(3(x+2)+1)=h(x+2+3)#

#g(3x+6+1)=h(x+5)#

#g(3x+7)=h(x+5)#...........#(2)#

Combining equations #(1)# and #(2)#, we get

#h(x+5)=f(x)#

Replace #x# by #(x-5)#

#h(x-5+5)=f(x-5)#

#h(x)=f(x-5)#

#QED#