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If f(x)=(2)/(3)x+(3)/(2),x""inR, then ...

If `f(x)=(2)/(3)x+(3)/(2),x""inR`,
then what is `f^(-1)(x)` equal to ?

A

`(2)/(3)x+(3)/(2)`

B

`(3)/(2)x-(9)/(4)`

C

`(2)/(3)x-(4)/(9)`

D

`(2)/(3)x-(2)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `f(x)=(2)/(3)x+(3)/(2)=y(say)=(4x+9)/(6)=y`
`implies4x+9=6y`
`impliesx=(6y-9)/(4)`
`x=f^(-1)(y)`
`impliesf^(-1)(x)=(6x-9)/(4)=(3x)/(2)-(9)/(4)`
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