Functions
Functional Equations / Odd-Even
MMTS_Full_Test_03
Grade 12
Question:
Let $f(x) = a\sin x + b\sqrt[3]{x+4}$. If $f\bigl(\log_{10}(\log_3 10)\bigr) = 5$ and $f\bigl(\log_{10}(\log_3 3)\bigr) = 3$, then $f\bigl(\log_{10}(\log_3 3)\bigr)$ is
Step-by-Step Solution
Key Concept: $\log_3 3 = 1$, so $\log_{10}(\log_3 3)=0$; directly evaluate $f(0)$.
$\log_3 3 = 1 \Rightarrow \log_{10}1 = 0$, so the second condition is $f(0) = b\cdot 4^{1/3}$. Also $\log_3 10 = 1/\log_{10}3$, and using symmetry of the function with the given values, $f(0)=3$ directly from the problem statement. Answer: 3.
Correct Answer: C