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Ipatiy [6.2K]
3 years ago
8

If f(x)= x/x-1 what is f^-1(x)

Mathematics
1 answer:
svp [43]3 years ago
8 0

Answer:

f^{-1}(x)=\frac{x}{x-1}

Step-by-step explanation:

our function is  

f(x)=\frac{x}{x-1}

we are asked to determine the inverse of the above function . In order to do so we put f(x) = y and separate x in terms of y and in the final answer , we replace x with y and x with h(x)

let us see how do we do that

y=\frac{x}{x-1}

multiplying both sides by (x-1)

y(x-1)=x

xy-y=x

subtracting x from both sides and adding y on both sides

xy-x=y

x(y-1)=y

dividing both sides by (y-1)

x=\frac{y}{y-1}

we now replace x with y and x with f^{-1}(x)


f^{-1}(x)=\frac{x}{x-1}

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