Question

If f(x) = 3x + 2 and g(x) = x2 + 1, which expression is equivalent to (fxg)(x)?

Answer 1

To find the expression equivalent to (f * g)(x), substitute g(x) into f(x) and simplify.

Step-by-step explanation:

To find the expression equivalent to (f × g)(x), we need to multiply the two given functions, f(x) = 3x + 2 and g(x) = x^2 + 1.

1. First, we substitute g(x) into f(x) and simplify:
   f(g(x)) = 3(g(x)) + 2
   f(g(x)) = 3(x2 + 1) + 2
   f(g(x)) = 3x2 + 3 + 2
   f(g(x)) = 3x2 + 5
2. Therefore, the expression equivalent to (f × g)(x) is 3x^2 + 5.

Answer 2

The quick answer I think will help you in the long run is that (f*g)(x) is just another way of saying f(x)*g(x). If that is enough, then ignore the rest of my response. Otherwise, keep reading.

For this problem

Step-by-step explanation:(f*g)(x) = f(x)*g(x)

You are given f(x) = 3x + 2 and g(x) = x^2 + 1. Simply substitute these expressions as follows:

f(x)*g(x) = (3x + 2)*(x^2 + 1)

Notice how I put each expression in parentheses. This practice will help immensely when dealing with more complicated expressions like this. Next, we simplify:

(3x + 2)*(x^2 + 1) = (3x)(x^2) + (3x)(1) + (2)(x^2) + (2)(1) <-- the foil method

= 3x^3 + 3x + 2x^2 + 2 <-- simplify each term

= 3x^3 + 2x^2 + 3x + 2 <-- reorganize and group like terms

hope this helped!