Prove That Function F : R → R, F(x) = 3 - 2x7 In - One - Toppr

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SolveGuidesJoin / LoginUse appLogin0You visited us 0 times! Enjoying our articles? Unlock Full Access!Standard XIIMathematicsDefinition of FunctionQuestionProve that function f:R→R,F(x)=3−2x7 in - one - one and onto. Also find f−1Open in AppSolutionVerified by Toppr

Given:-f(x)=3−2x7f:R→RLet f(x)=f(y)3−2x7=3−2y73−2x=3−2y⇒x=y∴f(x) is one-one.Now,Let y=f(x)y=3−2x77y=3−2x⇒x=3−7y2⇒g(x)=3−7x2g:R→RHence f(x) is one-one and onto.f−1x=g(x)=3−7x2.

Was this answer helpful?7Similar QuestionsQ1Prove that function f:R→R,F(x)=3−2x7 in - one - one and onto. Also find f−1View SolutionQ2prove that function "f" defined as f:R−(−2)→R−1,f(x)=xx+2 is one - one and onto. Also find f−1View SolutionQ3Prove that the function f:R→R given by f(x)=3x+3 is one-one and onto.View SolutionQ4If f:R−{3}→R−{5} is a function defined by f(x)=3x−3x−5, then show that f is one-one and onto and also find f−1View SolutionQ5Show that the function f:R→R defined by f(x)=3x−12,x∈R is one-one and onto functions. Also, find the inverse of the function f.View Solution

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