SOLUTION: I have tried very hard to solve this problem, but I'm stuck. Please help me solve this problem: g(x) = x -2 , f(x) = 3x - 2 , find x such that g(g(x)) = f(f(x))

Algebra ->  Rational-functions -> SOLUTION: I have tried very hard to solve this problem, but I'm stuck. Please help me solve this problem: g(x) = x -2 , f(x) = 3x - 2 , find x such that g(g(x)) = f(f(x))      Log On


   

Question 995666: I have tried very hard to solve this problem, but I'm stuck. Please help me solve this problem:
g(x) = x -2 , f(x) = 3x - 2 , find x such that g(g(x)) = f(f(x))
Found 2 solutions by MathLover1, algebrahouse.com:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29+=+x+-2 , f%28x%29+=+3x+-+2 ,
find x such that g%28g%28x%29%29+=+f%28f%28x%29%29
g%28g%28x%29%29+=+g%28x+-2%29
g%28g%28x%29%29+=+%28x+-2%29-2
g%28g%28x%29%29+=+x+-2-2
g%28g%28x%29%29+=+x+-4

f%28f%28x%29%29+=+f%283x+-+2%29
f%28f%28x%29%29+=+3%283x+-+2%29+-+2
f%28f%28x%29%29+=+9x+-+6+-+2
f%28f%28x%29%29+=+9x+-+8

g%28g%28x%29%29+=+f%28f%28x%29%29
+x+-4+=+9x+-+8
+8+-4+=+9x+-+x
+4+=+8x
+4%2F8=x
+highlight%28x=1%2F2%29

check:
g%28x%29+=+x+-2=>g%28x%29+=+1%2F2+-2=>g%28x%29+=+-3%2F2
g%28g%28x%29%29=g%28-3%2F2%29+
g%28g%28x%29%29=%28-3%2F2%29-2+
g%28g%28x%29%29=%28-3%2F2%29-4%2F2+
g%28g%28x%29%29=-7%2F2+

f%28x%29+=+3x+-+2
f%28x%29+=+3%281%2F2%29-+2
f%28x%29+=+3%2F2-+4%2F2
f%28x%29+=+-+1%2F2
+f%28f%28x%29%29=f%28-+1%2F2%29
+f%28f%28x%29%29=3%28-+1%2F2%29-2
+f%28f%28x%29%29=-+3%2F2-4%2F2
+f%28f%28x%29%29=-+7%2F2
so, g%28g%28x%29%29+=+f%28f%28x%29%29 for x=1%2F2

Answer by algebrahouse.com(1659) About Me  (Show Source):
You can put this solution on YOUR website!
g(x) = x - 2
f(x) = 3x - 2

g(g(x)) = (x - 2) - 2 {substituted (x - 2), in for x, into x - 2}
= x - 4 {combined like terms}

f(f(x)) = 3(3x - 2) - 2 {substituted (3x - 2), in for x, into 3x - 2}
= 9x - 6 - 2 {used distributive property}
= 9x - 8 {combined like terms}

If g(g(x)) = f((f(x)), then
x - 4 = 9x - 8 {set g(g(x)) equal to f(f(x))}
8x = 4 {subtracted x and added 8 to each side}
x = 1/2 {divided each side by 8}

For more help from me, visit: www.algebrahouse.com