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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Differentiation

NDA 2021 · Mathematics · Differentiation

Let f(x) be a polynomial function such that f ^ f(x)=x^4 . What is...

Let f(x)f(x) be a polynomial function such that f∘f(x)=x4f {}^{\circ} f(x)=x^4. What is f′(1)f^{\prime}(1) equal to?

Options

  1. A0
  2. B1
  3. C2
  4. D4

Correct answer

C. 2

Step-by-step solution

∴ Let f(x)=x2∴f[f(x)]=(x2)2=x4∴f′(x)=2xf′(1)=2\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}
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