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Transcript

Misc 1 Let f : R → R be defined as f(x) = 10x+ 7. Find the function g : R → R such that gof= fog= IR Here g is the inverse of f Finding inverse of f f(x) = 10x + 7 Let f(x) = y y = 10x + 7 y – 7 = 10x 10x = y – 7 x = (𝒚 − 𝟕)/𝟏𝟎 Let g(y) = (𝒚 − 𝟕)/𝟏𝟎 where g: R → R Now, we have to check the condition gof = fog = IR Finding gof gof = g(f(x)) = g(10x + 7) = ((10𝑥 + 7) − 7)/10 = (10𝑥 + 7 − 7)/10 = 10𝑥/10 = x = IR Finding fog fog = f(g(y)) = f((𝑦 − 7)/10) = 10 ((𝑦 − 7)/10) + 7 = y – 7 + 7 = y + 0 = y = IR Since gof = fog = IR, ∴ f is invertible & Inverse of f = g(y) = (𝒚 − 𝟕)/𝟏𝟎

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.