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Question: If \(f:R \rightarrow R,f(x) = (x + 1)^{2}\) and \(g:R \rightarrow R,g(x) = x^{2} + 1,\) then \(x = ...

If f:R→R,f(x)=(x+1)2f:R \rightarrow R,f(x) = (x + 1)^{2} and g:R→R,g(x)=x2+1,g:R \rightarrow R,g(x) = x^{2} + 1, then

x=0⇒f(x)=0x = 0 \Rightarrow f(x) = 0 is equal to

A

121

B

144

C

112

D

11

Answer

121

Explanation

Solution

fog(x)=f{g(x)}=f(x2+1)=(x2+1+1)2=(x2+2)2fog(x) = f\{ g(x)\} = f(x^{2} + 1) = (x^{2} + 1 + 1)^{2} = (x^{2} + 2)^{2}

⇒\Rightarrow f(x)=x−[x]f(x) = x - \lbrack x\rbrack.