Let IR be the set of all real numbers and for all x∈IR the mapping f:IR→IR is defined by f(x)=ax+3. If fof=I(IR), then find the value of a. Here I(IR) is the identity function.

Let IR be the set of all real numbers and for all x∈IR the mapping f:IR→IR is defined by f(x)=ax+3. If fof=I(I

Question 44 of 49

Q. Let IR be the set of all real numbers and for all x\inIR the mapping f:IR\toIR is defined by f(x)=ax+3. If fof=I(IR), then find the value of a. Here I(IR) is the identity function.

West Bengal WbchseWest Bengal HS (WBCHSE) Board 2025Subjective· 2mImportance★★★★★

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$f\circ f = I$ means composing $f$ with itself must give back $x$ for every $x$ ; match coefficients.

Given $f(x)=ax+3$ , compute the composition:

$f(f(x)) = a\big(ax+3\big)+3 = a^2x + 3a+3$

For $f\circ f = I_{\mathbb{R}}$ (the identity function), we need $f(f(x))=x$ for every $x$ , so matching coefficients:

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