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Misc 1 - Let f(x) = 10x+ 7. Find g such that gof = fog = IR - Finding Inverse

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  1. Chapter 1 Class 12 Relation and Functions
  2. Serial order wise
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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 Step 1 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: Y → N Step 2: gof = g(f(x)) = g(10x + 7) = 10𝑥 + 7﷯ − 7﷮10﷯ = 10𝑥 + 7 − 7﷮10﷯ = 10𝑥﷮10﷯ = x = IR Step 3: 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 − 3﷮4﷯

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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