Respuesta :
We are given the following function:
[tex]f\mleft(x\mright)=\frac{4}{x+2}-2[/tex]we are asked to determine the inverse of this function. To do that we will first change the "f(x)" for "y":
[tex]y=\frac{4}{x+2}-2[/tex]Now we will switch "x" and "y", like this:
[tex]x=\frac{4}{y+2}-2[/tex]Now we solve for "y", first by adding 2 to both sides:
[tex]x+2=\frac{4}{y+2}[/tex]Now we multiply both sides by "y+2":
[tex](y+2)(x+2)=4[/tex]Now we divide both sides by "x+2":
[tex]y+2=\frac{4}{x+2}[/tex]Now we subtract 2 to both sides:
[tex]y=\frac{4}{x+2}-2[/tex]Now we change "y" for the inverse of f(x), that is:
[tex]f^{-1}(x)=\frac{4}{x+2}-2[/tex]And thus we found the inverse. A similar procedure can be used for function 2.
