Final answer:
To find the constant k in the function g(x)=kx² given fg(2)=12, substitute x with 2 to get 4k=12 and solve for k, which results in k=3.
Step-by-step explanation:
The function given is g(x)=kx², where k is a constant. We also know that fg(2)=12. To find the value of k, we substitute x with 2 in the function g(x).
g(2)=k(2)²
Therefore, g(2)=4k. Since it is given that fg(2) is 12, we can deduce that fg(2) is actually g(2) and therefore:
4k = 12
To solve for k, we simply divide both sides of the equation by 4, leading to:
k = 12 / 4
k = 3
Hence, the constant k is equal to 3.