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Let $f: R \rightarrow R$ be a function defined by $f(x)=p x+q$ for all $x \in R$. Also fof = I. Find the value of p and q.
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written 3.1 years ago by
prajapatijaimin
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Solution:
$ \begin{aligned} \\ &\text { Here, } F \circ F=I \quad \text { (Given) } \\\\ &\quad F[F(x)]=I(x)=x \\\\ &\text { ie. } \quad F(p x+q)=x \\\\ &\Rightarrow \quad p(p x+q)+q=x \\\\ &\Rightarrow \quad p^2 x+p q+q=x \\\\ &\Rightarrow \quad p^2 x+p q+q-x=0 \\\\ &\Rightarrow \quad\left(p^2-1\right) x+q(p+1)=0\\ \end{aligned}\\ $ …
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