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Subjects
Class 12MathematicsRelations and FunctionsFunctionsHard
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If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=\frac{x-2}{3}), what is (f^{-1}(x))?

Answer and explanation

Correct answer: (3x+2)

Step 1: Let (y=\frac{x-2}{3}). Step 2: Then (3y=x-2), so (x=3y+2). Replacing (y) by (x), we get (f^{-1}(x)=3x+2). Step 3: To find an inverse, isolate (x) first and then interchange the variables.

Related tags

FunctionsInverseLinearRelations And FunctionsMathematicsClass 12 Mcq
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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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