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) ??

1 Answer
May 31, 2017

See proof below

Explanation:

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