Question

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

Answer 1

Answer:

The value of $f^{-1}(12)$ is $\frac{7}{-9}$ .

Step-by-step explanation:

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

$f(x)=3-\frac{7}{x}$

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

$\frac{7}{x} = 3 - f(x)$

$x = \frac{7}{3-f(x)}$

now, x = $f^{-1}(x)$ and f(x) be x.

Thus, $f^{-1}(x) = \frac{7}{3-x}$

Now, inserting value of x as 12,

$f^{-1}(12) = \frac{7}{3-(12)}$

$f^{-1}(12) = \frac{7}{-9}$

Answer 2

Answer:

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

Step-by-step 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 $xf(x)=3x-7$

⇒$xy=3x-7$

⇒$yx=3y-7$

⇒$3y-xy=7$

⇒$y(3-x)=7$

⇒$y=\frac{7}{3-x}$

Therefore, $f^{-1}(x)=\frac{7}{3-x}$

Now substitute x=12 in above equation,

$f^{-1}(12)=\frac{7}{3-12} =-\frac{7}{9}$