THE PROBLEM SOLVING

1. Make the graph of y = g(x). If the function h is defined by h(x) = g(2x) + 2, what is the value of h(1)?

Solution:
We are looking for h(1). We can get the first information from the graph of y = g(x) and the function of h(x) = g(2x) + 2. So, what’s the value of h(x) when x=1?
We substitute 1 into that situation
h(1) = g(2) + 2
Based on the graph above we find when x is equal to 2, y is equal to 1. Or we can say when x=2, g(x)=1, so h(1) = 1 + 2 = 3
Thus we get h(1) = 3

2. Let the function f be defined by f(x) = x + 1.
If 2f(p) = 20, what’s the value of f(3p)?

Solution:
We are looking for f(3p), it means that we are looking for the value of f(x) when x= 3p.
The first information is the function of f(x) = x + 1. And the next information is 2f(p) = 20. The question is “what’s f(x) when x = 3p”.
By using the function of 2f(p) = 20, we divide both side by 2, so we get f(p) = 10.
f(p) is just the implication of f(x) where x = p. We write
f(p) = 10
p + 1 = 10
p = 9
We are looking for the value of f(x) when x = 3p, so we can take p = 9 into x, thus x = 27.
We back to the first equation f(x) = x + 1. We substitute x = 27 into the equation, so that f(27) = 27 + 1 = 28.
So the value of f(3p) is 28.