SOLUTION: The function f is defined by f(x)=x^3 - 4x. The function of g is defined by g(x)=f(x+h)+k where h and k are constants. What is the value of hk? Points for y=f(x)are (-1,3),

Question 470687: The function f is defined by f(x)=x^3 - 4x. The function of g is defined by g(x)=f(x+h)+k where h and k are constants. What is the value of hk?
Points for y=f(x)are (-1,3), (1,-3)
Points for y=g(x) are (2,1), (4,-5)
The answer is 6, but I do not understand how they came up with this answer. Please help!
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

First and , and or

Looks to me like we have two equations for which means we can solve them as a system. Notice that contains but with a different input variable, namely .
To find we replace with wherever we find an in the equation.
will become

So now we replace in with our new result.

Also, we are given a pair of points that work with so lets plot them in and get a pair of equations. The first number in each point is and the second is .
Points in g(x) : (, ) and (, )
So for the first :

and for the second :

Notice that both long equations are equal to . That means they are also equal to each other.

So is , now we need .

So is . We already know that is . so :

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