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

Question

The functions f and g above are defined for all values of x. In the xy-plane, what is the y-coordinate of the point of intersection of the graphs of f and g?

Answer 1

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

Answer 2

f(x) = (1/3)x the fraction one third x

Answer 3

In that case, the problem simplifies to:

(x/3) + 3 = x -2
2x/3 = 5
x = 7.5
y = x-2 = 5.5