Question

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

(3x + 2)(x2 + 1)
3(x2 + 1) + 2
(3x + 2)2 + 1
3x2 +1 + 2

Answer 1

The expression equivalent to f(g(x)), with the given functions f(x) = 3x + 2 and g(x) = x^2 + 1, is 3x^2 + 5.

Step-by-step explanation:

To find the expression equivalent to f(g(x)), where f(x) = 3x + 2 and g(x) = x2 + 1, you substitute g(x) into the function f. This means every instance of x in the function f gets replaced with g(x).

The calculation is as follows:

f(g(x)) = f(x2 + 1) = 3·(x2 + 1) + 2

Then, you distribute the 3 into the parentheses:

= 3x2 + 3·1 + 2

= 3x2 + 5

Therefore, the expression equivalent to f(g(x)) with the given functions is 3x2 + 5.

Answer 2

3(x^2+1)+2

Step-by-step explanation:

since g(x) is equal to x^2+1 you can substitute x^2+1 for g(x) which will be f(x^2+1). then you can substitute f(x) for 3x+2 and in the end you will get 3(x^2+1)+2