Question

If f(x)=2|x+3|−1 and g(x)=−4x2−9, what is f(g(x))?

Answer 1

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Answer:

f(g(x)) = 8x^2 +11

Explanation:

Put the argument where the variable is and simplify.

f(g(x)) = f(-4x^2 -9) = 2|-4x^2 -9 +3| -1 = 2|-4x^2 -6| -1

The expression -4x^2 -6 is never positive, so the absolute value function just negates it:

f(g(x)) = 2(4x^2 +6) -1 = 8x^2 +12 -1

f(g(x)) = 8x^2 +11