Question

If f(x)=x+1/x-1. Prove that f(2x)=3f(x)+1/f(x)-3

Answer 1

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


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


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Then go to the claim that f(2x)=(3f(x)+1)/(f(x)+3) and plug in f(x) = (x-1)/(x+1) and simplify


f(2x)=(3f(x)+1)/(f(x)+3)


f(2x)=(3*(x-1)/(x+1)+1)/((x-1)/(x+1)+3)



f(2x)=(3*(x-1)+1(x+1))/(x-1+3(x+1)) ... multiply every term by the inner LCD x+1


f(2x)=(3x-3+x+1)/(x-1+3x+3)


f(2x)=(4x-2)/(4x+2)


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


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


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So this proves that f(2x)=(3f(x)+1)/(f(x)+3) is true when f(x)=(x-1)/(x+1) 

Answer 2

Answer:

Step-by-step explanation:

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

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

Then go to the claim that f(2x)=(3f(x)+1)/(f(x)+3) and plug in f(x) = (x-1)/(x+1) and simplify

f(2x)=(3f(x)+1)/(f(x)+3)

f(2x)=(3*(x-1)/(x+1)+1)/((x-1)/(x+1)+3)

f(2x)=(3*(x-1)+1(x+1))/(x-1+3(x+1)) ... multiply every term by the inner LCD x+1

f(2x)=(3x-3+x+1)/(x-1+3x+3)

f(2x)=(4x-2)/(4x+2)

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

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

So this proves that f(2x)=(3f(x)+1)/(f(x)+3) is true when f(x)=(x-1)/(x+1)