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If f(x)=(1/9x)-2 , what is f^–1(x)?

User Zeiger
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y= (1x/9)-2



y+2=1x/9


9(y+2)= x


f^-1 (x)= 9 (x+2)


?



y=1/9x -2


y+2= 1/9x



x= 1/9 (y+2)



f^-1 (x)= 1/9 (x+2)


User Simon GIS
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5 votes

Answer:


f^(-1)(x)=(1)/(9(x+2))

Explanation:

We have to find the inverse of the given function
f(x)=(1)/(9x)-2

1). We will rewrite the function in the form of a equation.


y=(1)/(9x)-2

2). Now we flip y by x and solve the equation for y.


x=(1)/(9y)-2


x+2=(1)/(9y)


9y(x+2)=1 [ By cross multiplication]


9y=(1)/((x+2))


y=(1)/(9(x+2))

3). Now we rewrite the equation in the form of a function.


f^(-1)(x)=(1)/(9(x+2))

Therefore, the answer is
f^(-1)(x)=(1)/(9(x+2))

User Sethunath K M
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