MATH SOLVE

5 months ago

Q:
# Let m(x) = x / xβ1a. Find the inverse of m.b. Graph m. How does the graph of m explain why this function is its own inverse?c. Think of another function that is its own inverse.

Accepted Solution

A:

Answer with Step-by-step explanation:We are given that a function [tex]m(x)=\frac{x}{x-1}[/tex]a.We have to find the inverse of m.Suppose, [tex]y=m(x)=\frac{x}{x-1}[/tex][tex]yx-y=x[/tex][tex]yx-x=y[/tex][tex]x(y-1)=y[/tex][tex]x=\frac{y}{y-1}[/tex]Replace x by y and y by x[tex]y=\frac{x}{x-1}[/tex]Substitute [tex]y=m^{-1}(x)[/tex][tex]g(x)=m^{-1}(x)=\frac{x}{x-1}[/tex]b.When the inverse function of given function is [tex]\frac{x}{x-1}[/tex]Then , we get fog(x)=[tex]f(g(x))=\frac{\frac{x}{x-1}}{\frac{x}{x-1}-1}[/tex][tex]fog(x)=\frac{x}{x-x+1}=x=I(x)[/tex]When f and g are inverse to each other then fog(x)=Identity function.c.If f(x)=xIt is self inverse function.