Final answer:
To find f(g(x)) in terms of x, we substitute g(x) into f(g) and simplify the expression. Given g(x) = -2x and f(g) = 2g^2, by substitution and simplification, we find that f(g(x)) = 8x^2.
Step-by-step explanation:
To find the function f(g(x)) in terms of x, we first need to identify what g(x) is. Given g(x) = -2x, we then substitute g(x) into f(g), where f(g) = 2g2. Substituting g(x) into f(g), we have f(-2x) = 2(-2x)2.
Next, we simplify the equation by squaring -2x which gives us f(-2x) = 2(4x2), since (-2x)(-2x) equals 4x2. Finally, multiplying 2 by 4x2 yields 8x2, which is the function f(g(x)) in terms of x.
Therefore, f(g(x)) = 8x2 when g(x) is substituted and the expression is simplified.