Answer:
[tex]\mathbf{ f(x+1)=7x-1}[/tex]
Step-by-step explanation:
We need to find f(x+1)
We are given:
[tex]g(x) - f(x) = -2x + 5\:and\:g(x) = 5x -3[/tex]
First we need to find f(x)
By putting value of g(x) into g(x)-f(x)
[tex]g(x) - f(x) = -2x + 5\\\Put\:value\:of\:g(x) = 5x -3\\5x-3-f(x)=-2x+5\\-f(x)=-2x+5-5x+3\\-f(x)=-2x-5x+5+3\\-f(x)=-7x+8\\f(x)=-(-7x+8)\\f(x)=7x-8\\[/tex]
We have, [tex]f(x)=7x-8[/tex]
Now finding f(x+1) by putting x=x+1
[tex]f(x)=7x-8\\Put\:x=x+1\\f(x+1)=7(x+1)-8\\f(x+1)=7x+7-8\\f(x+1)=7x-1[/tex]
So, [tex]\mathbf{ f(x+1)=7x-1}[/tex]
