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If f(x)=(2x)/(5)+(7)/(3), f^(-1)(x)=...

If `f(x)=(2x)/(5)+(7)/(3), f^(-1)(x)=`

A

`(15)/(6x+35)`

B

`(6)/(15x+35)`

C

`(15x-6)/(35)`

D

`(15x-35)/(6)`

Text Solution

Verified by Experts

The correct Answer is:
D
To find the inverse function `f^(-1)(x)` of `f(x)=(2x)/(5)+(7)/(3)`, write the inverse function as an equation `x =(2y)/(5)+(7)/(3)`, and solve for y.
`15x = 15((2y)/(5)+(7)/(3))`
`15x = 6y + 35`
`15x - 35=6y`
`y = (15x-35)/(6)`
So `f^(-1)(x)=(15x-35)/(6)`.
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