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

(f o g)(x) = 3x^2 + 5

Step-by-step explanation:

(f o g)(x) is a composite function in which g(x) = x^2 + 1 becomes the input to f(x) = 3x + 2.

Write out f(x) = 3x + 2 leaving a blank for each x:

f(    ) = 3(    ) + 2

Now insert g(x) into the first set of parentheses and x^2 + 1 into the second:

(f o g)(x) = 3(x^2 + 1) + 2, or, after simplification,

(f o g)(x) = 3x^2 + 5

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