Question

Given: f(x) = x^2 + 3x + 1 and g(x) = 2x − 3

Choose all that correctly evaluates the combined functions:

Answer 1

To evaluate the combined functions f(g(x)), substitute the expression for g(x) into f(x) and simplify.

Step-by-step explanation:

To evaluate the combined functions f(g(x)), we substitute the expression for g(x) into f(x). So, we have:

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

Expanding and simplifying further:

= 4x^2 - 12x + 9 + 6x - 9 + 1

= 4x^2 - 6x + 1

Therefore, the correct evaluation of the combined functions is f(g(x)) = 4x^2 - 6x + 1.