Question

Let $f(x) = x^3$ and $g(x) = 3^x$. The values of $a$ such that $g(f(a)) = f(g(a))$ are:

• A. $0, 2$
• B. $1, 3$
• C. $0, \pm 3$
• D. $1, \pm 2$
• E. $0, \pm \sqrt{3}$

Hint:

Remember to use the law of exponents $(x^m)^n = x^{mn}$ when calculating $f(g(a))$. A common mistake is to write $3^{a^3}$ for both compositions, but the placement of the power matters significantly in exponentiation.

Answer 1

The Correct Option is C