Q242 / 270 · NDA 2019 (Phase 2) · Mathematics

Paragraph: Let $f(x)=x^2+2 x-5$ and $g(x)=5 x+30$
Question: Consider the following statements: 1. $f[g(x)]$ is a polynomial of degree 3 . 2. $g[g(x)]$ is a polynomial of degree 2 . Which of the above statements is/are correct?

  • A
    1 only
  • B
    2 only
  • C
    Both 1 and 2
  • Correct answer
    D
    Neither 1 nor 2

Solution

(i) $f(g(x))=(5 x+30)^2+2(5 x+30)-5$ $\Rightarrow f(g(x))$ is second degree. (ii) $g(g(x))=5(5 x+30)+30$ $\Rightarrow g(g(x))$ is first degree $\therefore$ both statements are wrong.

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

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