Q238 / 270 · NDA 2021 (Phase 2) · Mathematics

Let $f(x)$ be a polynomial function such that $f \circ f(x)=x^4$. What is $f^{\prime}(1)$ equal to?

  • A
    0
  • B
    1
  • Correct answer
    C
    2
  • D
    4

Solution

$\begin{aligned} & \therefore \text { Let } f(x)=x^2 \\ & \therefore f[f(x)]=\left(x^2\right)^2=x^4 \\ & \therefore f^{\prime}(x)=2 x \\ & f^{\prime}(1)=2\end{aligned}$

Hence, the correct answer is option: 'C'.

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