If f(x) = 1/3x - 7, find f^-1(x).

aruv | Student


By def of inverse function





`f^(-1)(y)=x `     (i)






sbstitute x in (i)


Thus inverse of f is



llltkl | Student

If `f(x)=1/(3x)-7`

Put `y=1/(3x)-7`

Interchange x and y,


`rArr 1/(3y)=x+7`

`rArr 3y=1/(x+7)`

`rArr y=1/(3x+21)`

So, `f^(-1)(x)=1/(3x+21)`


Check: `f(f^(-1)(x))=1/(3(1/(3x+21)))-7=1/(1/(x+7))-7=x+7-7=x`



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