Given g(x)=3x+4 and h(x)=sqrt x-3 find and simplify. State domain when necessary.
Solve 2g(3)+h(12)
First, let's find g(3) and h(12).
g(3) = 3(3) + 4 = 9 + 4 = 13
h(12) = √12 - 3 = 2√3 - 3
Now we can substitute these values back into the original expression.
2g(3) + h(12) = 2(13) + (2√3 - 3) = 26 + 2√3 - 3 = 23 + 2√3
Therefore, 2g(3) + h(12) simplifies to 23 + 2√3.
The domain of h(x) = √x - 3 is x ≥ 0 because the square root of a negative number is not defined for real numbers.