My problem is the following: Let the functions: f(x)= 2^(x+3) -5 and g(x)=3x+3
a)For what values of x is f(x)=g(x)?
I tried to solve for x, but I really cannot, is it possible to solve without Desmos?
Thanks,
Thomas Charland
The equation they want you to solve, f(x) = g(x), is 2^(x+3) -5 = 3x+3. This is a transcendental equation, which
can't be solved by algebraic methods; but as was mentioned, there are "numerical methods" to find an
approximate solution to any equation (and sometimes they accidentally find an
exact solution).
The simplest numerical method is "guess and check". Just try some numbers and see if they make it true -- for example, try x = 0, 1, 2, ... . Then try simple negative numbers. If one of those is a solution, you're ready for the next step. If not, you can try to narrow down a solution, by finding numbers between which there has to be a solution, and then trying numbers that are closer together. (The more advanced numerical methods just make that process more efficient by giving you a good guess for the next step each time.)
Of course, that can't tell you whether you have found
all the solutions. One way to do that is to sketch the graph yourself (e.g. using calculus to find maxima and minima), and use what you discover in that process to decide whether there can be other solutions, and where they would be. You don't need to be dependent on technology to do your graphing for you! (Incidentally, just graphing by plotting points can amount to guess-and-check, so you might want to start there.)
EDIT: I've given you a better hint here than you may realize. Be sure to try what I've suggested!