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Misc 1 Let f : R β†’ R be defined as f(x) = 10x+ 7. Find the function g : R β†’ 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 = (π’š βˆ’ πŸ•)/𝟏𝟎 Let g(y) = (π’š βˆ’ πŸ•)/𝟏𝟎 where g: R β†’ R Now, we have to check the condition gof = fog = IR Finding gof gof = g(f(x)) = g(10x + 7) = ((10π‘₯ + 7) βˆ’ 7)/10 = (10π‘₯ + 7 βˆ’ 7)/10 = 10π‘₯/10 = x = IR Finding fog fog = f(g(y)) = f((𝑦 βˆ’ 7)/10) = 10 ((𝑦 βˆ’ 7)/10) + 7 = y – 7 + 7 = y + 0 = y = IR Since gof = fog = IR, ∴ f is invertible & Inverse of f = g(y) = (π’š βˆ’ πŸ•)/𝟏𝟎

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.