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Class 12MathematicsRelations and FunctionsFunctionsHard
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If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are such that (f(x)=x^2+1) and (g(x)=3x-2), what is ((f\circ g)(x))?

Answer and explanation

Correct answer: (9x^2-12x+5)

Step 1: ((f\circ g)(x)) means (f(g(x))). Step 2: Substitute (g(x)=3x-2) into (f), giving ((3x-2)^2+1=9x^2-12x+5). Step 3: In composition, the order matters.

Related tags

CompositionFunction-CompositionPolynomialFunctionsRelations And FunctionsMathematicsClass 12 Mcq
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  1. 1If (f:A\to B) is a function, what condition is necessary for every element of (A)?
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  3. 3In a function (f:A\to B), what is (A) called?
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  6. 6If (f={(1,2),(2,4),(3,6)}), what is the range of (f)?
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