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Directions: Read the following information and answer the three items that follow:
Let f(x) = x2 + 2x – 5 and g(x) = 5x + 30
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
  • d)
    Neither 1 nor 2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Directions: Read the following information and answer the three items ...
Given: f(x) = x2 + 2x – 5 and g(x) = 5x + 30
⇒ f[g(x)] = f(5x + 30) = (5x + 30)2 + 2(5x + 30) – 5 = 25x2 + 310x + 955
⇒ f[g(x)] is a polynomial of degree 2.
Hence statement 1 is false.
⇒ g[g(x)] = g(5x + 30) = 5(5x + 30) + 30 = 25x + 180
⇒ g[g(x)] is a polynomial of degree 1.
Hence statement 2 is wrong.
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Directions: Read the following information and answer the three items that follow:Let f(x) = x2 + 2x – 5 and g(x) = 5x + 30Consider 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 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'D'. Can you explain this answer?
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