Functions Help, Please?

Question

f(x) = (x) / (x-2)
g(x) = (5-x) / (5+x)

I am to plug f(x) and g(x) into f(x+1)g(x+1) to solve for a rational function.

I know how to multiply out the f(x) by the g(x), but I don't know how to change the original f(x) and g(x) into f(x+1) and g(x+1).

I hope I am making sense, thank you for your help.

Answer 1

All you are doing is replacing x with x+1
eg. f(x)=x/x-2 hence
f(3) =2/3-2 =2/1 =2 s0,
f(x+1)= (x+1)/x+1-2
= x+1/x-1
likewise g(x) = 5-x/5+x
g(x+1) = [5- (x+1)]/5+(x+1)
= 5 -x -1/ 5+x+1
= 4-x/6+x

Answer 2

f(x+1) = (x+1) /( x+1-2)
= (x+1)/(x-1)

g(x+1) = ( 5- x-1) /( 5+ x+1)
= (4-x)/( 6+x)

Answer 3

f(x + 1) = (x + 1) / (x - 1)
g(x + 1) = (4 - x) / (6 + x)
Product
(x + 1).(4 - x) / (x - 1).(x + 6)

Answer 4

just replace x by (x+1)
so,
f(x+1) = (x+1) / [(x+1)-2]
=(x+1)/(x-1)


and
g(x+1)=[5-(x+1)] / [5+(x+1)]
=(4-x)/(x+6)


f(x+1) * g(x+1)= [-(x*x) +3x +4] / [(x*x) + 5x-6]