निम्नलिखित फलनों का प्रतिलोम फलन ज्ञात कीजिए -
`(i) f(x)=-(1)/(3)x+4" "(ii) f(x)=(x-1)/(x+1) " " (iii) f(x)=sqrt(1-x^(2)),0 le x le 1`

Answer

`(i) 12-3x (ii) (1+x)/(1-x) (iii) sqrt(1-x^(2))`

Explanation

(i) `f(x)=-(1)/(3)x+4 rArr y=-(1)/(3)+x rArr y-4=-(1)/(3) x`
`rArr x=-3(y-4) rArr f^(-1)(y)=-3(y-4) `
`rArr f^(-1)(x)=-3(x-4)=12-3x`
(ii) `f(x)=(x-1)/(x+1) rArr y=(x-1)/(x+1) rArr x=(y+1)/(1-y)` अतः `f^(-1)(y)=(1+y)/(1-y)`
i.e., `f^(-1)(x)=(1+x)/(1-x)`