Answer:
To find f(g(x)), substitute g(x) into f, yielding f(g(x)) = f(x´) = 2(x´)³. By applying the exponent rule, we get 2x^(4*3) = 2x··, which makes option 3) 2x·· the correct choice.
Explanation:
To find f(g(x)), we first need to determine what g(x) is and then apply the function f to that result. Since g(x) = x´, we substitute g(x) into the function f, obtaining f(g(x)) = f(x´).
Now, we apply the function f which is given by f(x) = 2x³, to x´. Substituting x´ into the function f, we get:
f(g(x)) = f(x´) = 2(x´)³
To solve this, we multiply the exponent 4 by the exponent 3, following the rule of exponents for raising a power to a power: x^(a*b) = x^(ab).
Thus:
f(g(x)) = 2(x´)³ = 2x^(4*3) = 2x··
The correct choice from the given options is therefore 3) 2x··.