Answer
$(f \circ g)(x) = 3x^2 + 1$
Work Step by Step
This exercise asks us to take the inner function and plug it into the outer function. Let's write out the problem:
$(f \circ g)(x) = f(g(x)) = 3(x^2 + 1) - 2$
Distribute the terms:
$(f \circ g)(x) = f(g(x)) = 3(x^2) + (3)(1) - 2$
Multiply to simplify:
$(f \circ g)(x) = f(g(x)) = 3x^2 + 3 - 2$
Combine like terms:
$(f \circ g)(x) = f(g(x)) = 3x^2 + 1$
