If h(x) = f(x)g(x) and f(x) = 2x +5, determine g(x).
I'm given h(x) = 6x + 15.
I know I can divide h(x) by f(x), but I have no idea on how to continue on from there?
Thank you! :)
+9466 \(\ h(x)\ =\ f(x)\cdot g(x)\)
Divide both sides of the equation by f(x)
\(\dfrac{h(x)}{f(x)}\ =\ g(x)\)
Substitute 6x + 15 in for h(x) and substitute 2x + 5 in for f(x)
\(\frac{6x+15}{2x+5}\ =\ g(x)\)
That is the same as....
\(g(x)\ =\ \frac{6x+15}{2x+5}\)
We can factor 3 out of 6x + 15 because 3(2x + 5) = 6x + 15
\(g(x)\ =\ \frac{3(2x+5)}{2x+5}\)
Cancel the common factor of (2x + 5) in the numerator and denominator.
\(g(x)\ =\ 3\) and note that 2x + 5 ≠ 0 so x ≠ -5/2
So we can say g(x) = 3 for all possible values of x except x = -5/2
