Question

Let m(x) = x / x−1

Answer 1

Answer with Step-by-step explanation:

We are given that a function

$m(x)=\frac{x}{x-1}$

a.We have to find the inverse of m.

Suppose, $y=m(x)=\frac{x}{x-1}$

$yx-y=x$

$yx-x=y$

$x(y-1)=y$

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

Replace x by y and y by x

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

Substitute $y=m^{-1}(x)$

$g(x)=m^{-1}(x)=\frac{x}{x-1}$

b.When the inverse function of given function is $\frac{x}{x-1}$

Then , we get fog(x)=$f(g(x))=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-1}$

$fog(x)=\frac{x}{x-x+1}=x=I(x)$

When f and g are inverse to each other then fog(x)=Identity function.

c.If f(x)=x

It is self inverse function.