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

Step-by-step explanation:

The given functions are

and

By the algebraic properties of functions:

We just have to substitute to obtain:

The first choice is correct.

take the logarithm of both sides (the base of the log doesn't matter):

apply the exponent property - this says that :

distribute the log terms on both sides:

group like terms together:

divide through both sides by the coefficient on :

you can do some additional rewriting here using the properties of the logarithm to simplify things if you like:

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