Question

At which x value will f(x)=3x+3 exceed g(x)=3x+10

Answer 1

There are no x value that allows f(x) to exceed g(x). f(x) is parallel to g(x) and it will always be 7 less than g(x).

Answer 2

We write an inequality:

$f(x) > g(x)$

$3^x + 3 > 3x + 10$

$3^x > 3x + 7$

This equation cannot be solved using trivial methods found in high-school classes, so we resort to graphical examination.  $3x+7$ is a linear function while $3^x$ is an exponential one (with limit zero as $x$ approaches $- \infty$).  We see that $3^x = 3x+7$ at approximately $x=2.4$ and $x=-2.3$.

Indeed, using a computer algebra system such as the ones on modern TI calculators and on many internet sites gives equality at $x=2.42, -2.31$.  By observing our graph, we see that $f(x) > g(x)$ when $x > 2.42$ or $x < -2.31$.