Posted by Samantha on Wednesday, July 11, 2012 at 4:08am.
f(x) = 1/3x + 3 and g(x) = x  2
The functions f and g above are defined for all values of x. In the xyplane, what is the ycoordinate of the point of intersection of the graphs of f and g?

Math  drwls, Wednesday, July 11, 2012 at 6:43am
It is not clear if the x in the f(x) equation is in the denominator.
I assume you mean
f(x) = 1/(3x) + 3, and not
x/3 + 3.
f(x) = g(x) when
1/(3x) + 3 = x 2
1/(3x) = x  5
3x^2 15x 1 = 0
Solve for x. There will be two answers.
x = (1/6)[15 +/ sqrt(225+12)]
= 5.066 or 0.0658

Math  Samantha, Wednesday, July 11, 2012 at 7:07am
f(x) = (1/3)x the fraction one third x

Math  drwls, Wednesday, July 11, 2012 at 8:15am
In that case, the problem simplifies to:
(x/3) + 3 = x 2
2x/3 = 5
x = 7.5
y = x2 = 5.5
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