Question

Find f^-1 (12) if x f(x)=3x-7

Answer 1

f^-1(12)=-7/9

Explanation:

To find the inverse of a function, say f(x), follow these steps

• Replace f(x) with y. this will make further solving easier.
• Replace x with y and y with x.
• Solve for y with the above equation we got in step 2.
• Replace y with
  `f^(-1)(x)`

So the given equation is
`xf(x)=3x-7`

⇒
`xy=3x-7`

⇒
`yx=3y-7`

⇒
`3y-xy=7`

⇒
`y(3-x)=7`

⇒
`y=(7)/(3-x)`

Therefore,
`f^(-1)(x)=(7)/(3-x)`

Now substitute x=12 in above equation,

`f^(-1)(12)=(7)/(3-12) =-(7)/(9)`

Answer 2

The value of
`f^(-1)(12)` is
`(7)/(-9)` .

Explanation:

The given equation is
`x f(x) = 3x-7` .

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

The inverse of the function is found by adjusting the equation such that, expressing x in terms of f(x).

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

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

now, x =
`f^(-1)(x)` and f(x) be x.

Thus,
`f^(-1)(x) = (7)/(3-x)`

Now, inserting value of x as 12,

`f^(-1)(12) = (7)/(3-(12))`

`f^(-1)(12) = (7)/(-9)`