Question

Given that f(x)=2x/3 evaluate f^-1(6)

Answer 1

9

Explanation:

we know by definition that

`f^(-1)(f(x))=x\\\\f^(-1)((2x)/(3))=x\\\\f^(-1)(x)=ax\\\\f^(-1)((2x)/(3))=a((2x)/(3))=x\\\\f^(-1)(x)=(3x)/(2)`

so now we evaluate

`f^(-1)(6)=(3*6)/(2)\\\\=3*3\\\\f^(-1)(6)=9`

and if we want to do an extra step

`f^(-1)(f(6))=6\\\\f^(-1)((2*6)/(3))=f^(-1)(4)=(3*4)/(2)=6`

which works.