Respuesta :

SageRage

Answer:

Yes

Step-by-step explanation:

  • if [tex]f(x)=\frac{1}{2}x-2[/tex] then what is [tex]f^-1(x)[/tex]  (the inverse of f(x)? let's find out
  • [tex]f(x)=\frac{1}{2}x-2\\y=\frac{1}{2}x-2[/tex] make f(x) into y
  • Then make y into x and make x into y so [tex]x=\frac{1}{2}y-2[/tex]
  • [tex]x=\frac{1}{2}y-2[/tex] now get the new y on the left and everything else on the right
  • [tex]x=\frac{1}{2}y-2\\x+2=\frac{1}{2}y\\2(x+2)=(2)\frac{1}{2}y\\y=2x+4[/tex] now make y = g(x)
  • [tex]g(x)=2x+4[/tex]
  • So you found the inverse of f(x) and it is the same as g(x), so the functions are inverses of each other

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