Respuesta :
Answer:
The value of [tex]f^{-1}(12)[/tex] is [tex]\frac{7}{-9}[/tex] .
Step-by-step explanation:
The given equation is [tex]x f(x) = 3x-7[/tex] .
[tex]f(x)=3-\frac{7}{x}[/tex]
The inverse of the function is found by adjusting the equation such that, expressing x in terms of f(x).
[tex]\frac{7}{x} = 3 - f(x)[/tex]
[tex]x = \frac{7}{3-f(x)}[/tex]
now, x = [tex]f^{-1}(x)[/tex] and f(x) be x.
Thus, [tex]f^{-1}(x) = \frac{7}{3-x}[/tex]
Now, inserting value of x as 12,
[tex]f^{-1}(12) = \frac{7}{3-(12)}[/tex]
[tex]f^{-1}(12) = \frac{7}{-9}[/tex]
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 [tex]f^{-1}(x)[/tex]
So the given equation is [tex]xf(x)=3x-7[/tex]
⇒[tex]xy=3x-7[/tex]
⇒[tex]yx=3y-7[/tex]
⇒[tex]3y-xy=7[/tex]
⇒[tex]y(3-x)=7[/tex]
⇒[tex]y=\frac{7}{3-x}[/tex]
Therefore, [tex]f^{-1}(x)=\frac{7}{3-x}[/tex]
Now substitute x=12 in above equation,
[tex]f^{-1}(12)=\frac{7}{3-12} =-\frac{7}{9}[/tex]
