SOLUTION: Please solve and then tell if a function or not Thank you so much!! f(x) =3x-2 g(x)=x^2-3x FIND: (fog)(x) thank you

Algebra ->  Functions -> SOLUTION: Please solve and then tell if a function or not Thank you so much!! f(x) =3x-2 g(x)=x^2-3x FIND: (fog)(x) thank you      Log On


   

Question 88250: Please solve and then tell if a function or not
Thank you so much!!
f(x) =3x-2
g(x)=x^2-3x
FIND: (fog)(x)
thank you
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Please solve and then tell if a function or not
f(x) =3x-2
g(x)=x^2-3x
FIND: (fog)(x) = f[x^2-3x] = 3(x^2-3x)-2 = 3x^2-9x-2
Since, for every x value there is only one y value, fog(x) is a function.
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Cheers,
Stan H.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
fog%28x%29=f%28g%28x%29%29

f%28g%28x%29%29=f%28x%5E2-3x%29 F of G of x is equivalent to F of x%5E2-3x

f%28x%5E2-3x%29=3%28x%5E2-3x%29-2 Now plug in x=x%5E2-3x into f%28x%29

f%28x%5E2-3x%29=3x%5E2-3%283x%29-2 Distribute

f%28x%5E2-3x%29=3x%5E2-9x-2 Multiply

So f%28g%28x%29%29 is a function