AP EAMCET202018 Sep 2020Morning ShiftMathematicsFunctionsActual
Find the function (g(t) ) if (f(t)=3 t-2 ) and ((g f)⁻¹(t)=t-2 ).
Options
- A(g(t)= (t-8) 3 )
- B(g(t)= (t+8) 3 )
- C(g(t)= (8-t) 3 )
- D(g(t)=3 t-8 )
Correct answer
B. (g(t)= (t+8) 3 )
Step-by-step solution
Given, ((g f)⁻¹(t)=t-2 ) ( aligned & (g f)(t)=t+2 & g(f(t))=t+2 & g(3 t-2)=(t+2) f(t)=3 t-2 aligned ) Now replace (t ) by ( t 3 ), we get (g(t-2)= ( t 3 +2 ) ) Again replace (t ) by (t+2 ), we get (g(t)= t+2 3 +2= t+8 3 )