Respuesta :
f(x) = 1/9x+2
-2 from both sides
f(x)-2 = 1/9x
*2 to both sides
9(f(x)-2) = x
replace 'f(x)' with 'x'
9(x-2) = f(x^-1)
simplify and reverse sides
f(x)^-1 = 9x-18
-2 from both sides
f(x)-2 = 1/9x
*2 to both sides
9(f(x)-2) = x
replace 'f(x)' with 'x'
9(x-2) = f(x^-1)
simplify and reverse sides
f(x)^-1 = 9x-18
Answer:
[tex]f^{-1}(x)=9x-18[/tex]
Step-by-step explanation:
we have
[tex]f(x)=\frac{1}{9}x+2[/tex]
Let
[tex]y=f(x)[/tex]
[tex]y=\frac{1}{9}x+2[/tex]
Exchange variables x for y and y for x
[tex]x=\frac{1}{9}y+2[/tex]
Isolate the variable y
[tex]x-2=\frac{1}{9}y[/tex]
[tex]y=9(x-2)[/tex]
[tex]y=9x-18[/tex]
Let
[tex]f^{-1}(x)=y[/tex]
[tex]f^{-1}(x)=9x-18[/tex] -------> inverse function