Read the following information and answer the three items that follow :
Let $f (x) = x^{2} + 2 x - 5$ and $g (x) = 5 x + 30$
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 ?

1 only

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2 only

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Both 1 and 2

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Neither 1 nor 2

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Solution

The correct option is C Neither 1 nor 2
Neither 1 nor 2

Given,

$f (x) = x^{2} + 2 x - 5$

$g (x) = 5 x + 30$

(i)

$f [g (x)]$

$= f [5 x + 30]$

$= (5 x + 30)^{2} + 2 (5 x + 30) - 5$

upon solving the above equation, we get,

$f [g (x)] = 25 x^{2} + 310 x + 955$

degree $= 2$

(ii)

$g [g (x)]$

$= g [5 x + 30]$

$= 5 (5 x + 30) + 30$

$= 25 x + 150 + 30$

$= 25 x + 180$

$g [g (x)] = 25 x + 180$

degree $= 1$

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Question 1 (i)
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be defined by

f (x) = {\begin{matrix} g (x), & x \leq 0 | x |^{s i n x}, & x > 0 \end{matrix}

f (x)

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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 ?

The correct option is C Neither 1 nor 2Neither 1 nor 2Given,f(x)=x2+2x−5g(x)=5x+30(i)f[g(x)]=f[5x+30]=(5x+30)2+2(5x+30)−5upon solving the above equation, we get,f[g(x)]=25x2+310x+955degree =2(ii)g[g(x)]=g[5x+30]=5(5x+30)+30=25x+150+30=25x+180g[g(x)]=25x+180degree =1

Read the following information and answer the three items that follow :
Let $f (x) = x^{2} + 2 x - 5$ and $g (x) = 5 x + 30$
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 ?