shivraj
Given f(x)=x^21 and g(x)=x+1, find (fog)(x)?



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sauravshakya
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(fog)(x) = f(g(x)) = f(x+1)

sauravshakya
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@shivraj u got what I did??????

shivraj
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no sir

miteshchvm
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that means you need to put
x= x + 1 in f(x)

sauravshakya
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Yep:
(fog)=f(g(x))

sauravshakya
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Now, substitute there g(x)

miteshchvm
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suppose f(1) = 0
f(x) = x^2  1
f[g(x)] = (x+1)^2  1

shivraj
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ok

miteshchvm
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you got it? @shivraj

shivraj
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yep

godfreysown
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if \[f(x)=x^21\ and \ g(x)=x+1, \\ \ then \ (fog)'(x)=\ (by \ product \ rule)\ u'v+u'v, \\where\ u=f(x); \ v=g(x) \\ \therefore\ (x^21)(1)+(2x)(x+1)=\\x^21+2x^2+2x=\\3x^2+2x1=\\(3x1)(x+1) \]

shivraj
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thnks godfreysown