Question
Download Solution PDFComprehension
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?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
If p(x) = a0 + a1 x + …… + anxn , where coefficients of x are real and if an ≠ 0 .Then p(x) is a polynomial of degree n.
Calculation:
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.Last updated on May 30, 2025
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