Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Finding Inverse
Inverse of a function
How to check if function has inverse? Deleted for CBSE Board 2024 Exams
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How to find Inverse?
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Finding Inverse
Last updated at May 29, 2023 by Teachoo
Question 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 β 7 = 10x 10x = y β 7 x = (π β π)/ππ Let g(y) = (π β π)/ππ 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) β 7)/10 = (10π₯ + 7 β 7)/10 = 10π₯/10 = x = IR Finding fog fog = f(g(y)) = f((π¦ β 7)/10) = 10 ((π¦ β 7)/10) + 7 = y β 7 + 7 = y + 0 = y = IR Since gof = fog = IR, β΄ f is invertible & Inverse of f = g(y) = (π β π)/ππ