f(x) = 3x + 5, g(x) = 6x^2
Find (fg)(x)
(fg)(x)
=f(g(x))
=f(6x²)
=3(6x²)+5
simplify to get final answer.
To find (fg)(x), we need to multiply the two functions f(x) and g(x) together.
First, let's compute f(x) * g(x):
f(x) * g(x) = (3x + 5) * (6x^2)
To multiply these two expressions, we will use the distributive property of multiplication:
f(x) * g(x) = 3x * (6x^2) + 5 * (6x^2)
Now, let's simplify each term separately:
1. Simplifying the first term: 3x * (6x^2)
Multiply the coefficients (3 * 6) and add the exponents (x * x^2):
3x * (6x^2) = 18x^(1+2) = 18x^3
2. Simplifying the second term: 5 * (6x^2)
Multiply the coefficients (5 * 6):
5 * (6x^2) = 30x^2
Now, we add the simplified terms together:
f(x) * g(x) = 18x^3 + 30x^2
So, (fg)(x) = 18x^3 + 30x^2.