Adi3
  • Adi3
Will medal please help find the inverse of g(x) = (1)/x-1 + 3
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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Adi3
  • Adi3
\[\left(\begin{matrix}\\ \frac{ 1}{ x-1 }\end{matrix}\right) + 3\]
Adi3
  • Adi3
\[\frac{ 1 }{ x-1} + 3\]
Adi3
  • Adi3
if this more clear

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Nnesha
  • Nnesha
g(x) is same as y so you can replace g(x) with y \[\huge\rm \color{ReD}{y}=\frac{ 1 }{ \color{blue}{x}-1 } +3\] to find inverse `switch x and y` \[\huge\rm \color{blue}{x}=\frac{ 1 }{ \color{red}{y}-1 } +3\] now solve for y
Adi3
  • Adi3
ok, x - 3 = \[\frac{ 1 }{ y-1 }\]
Adi3
  • Adi3
is that right
Adi3
  • Adi3
@IrishBoy123
Adi3
  • Adi3
@HELPMEPLZ!!
Adi3
  • Adi3
still on inverse, this is too much for me
Nnesha
  • Nnesha
sorry i was afk yes that's right \[\huge\rm x-3=\frac{ 1 }{ y-1}\] now how would you cancel out y-1 from right side ?
Adi3
  • Adi3
divde it?
imqwerty
  • imqwerty
write y in terms of x and then jst switch y and x :) function which u get is inverse
Nnesha
  • Nnesha
its already divided by 1 (1/y-1 )to cancel it out you should do opposite of division
Adi3
  • Adi3
multiply
Nnesha
  • Nnesha
yes right multiply both sides by y-1
Adi3
  • Adi3
so 1x-3
Nnesha
  • Nnesha
multiply `both sides` by y-1 \[\huge\rm (y-1) (x-3)=\frac{ 1 }{\cancel{y-1} } \times \cancel{(y-1)}\] we can cancel out y-1 \[\large\rm (y-1)(x-3)=1\] now again to solve for y move `x-3` to the right side
Adi3
  • Adi3
ohh, then how to get y by itself?
Nnesha
  • Nnesha
how would you cancel x-3 from left side ?
Adi3
  • Adi3
divide
Nnesha
  • Nnesha
right so divide both sides by x-3 let me know what you get
Nnesha
  • Nnesha
it's multiplication( y-1 ) times (x-3) so yes you should divide
Adi3
  • Adi3
y-1 = 1/x-3
Nnesha
  • Nnesha
right whats nexxt ?
Adi3
  • Adi3
y = 1/x-3 + 1
Nnesha
  • Nnesha
right now we should get the common denominator |dw:1443366122753:dw|
Adi3
  • Adi3
OK, Can i ask a last question
Adi3
  • Adi3
pls
imqwerty
  • imqwerty
yea y nt :)
Nnesha
  • Nnesha
yes ?
Adi3
  • Adi3
ok, thank you all. find the inverse of \[-\frac{ 2 }{ 5}x - 2\]
Adi3
  • Adi3
g(x) =
Nnesha
  • Nnesha
same steps try it first
Adi3
  • Adi3
x+2 = -2/5y
imqwerty
  • imqwerty
yea nxt
Adi3
  • Adi3
thts wht idk
imqwerty
  • imqwerty
think a way to isolate y
Nnesha
  • Nnesha
now \[x+2 =\frac{ -2 }{ 5 }y\] what would be the nexxt step ?
Adi3
  • Adi3
divide?
imqwerty
  • imqwerty
divide by what..
Nnesha
  • Nnesha
right divide what ?
Adi3
  • Adi3
idk
Adi3
  • Adi3
-2/5
Nnesha
  • Nnesha
well first you need to get rid of the fraction
imqwerty
  • imqwerty
if u have 2x and u want just x then what number will u divide it by?
Nnesha
  • Nnesha
\[\huge\rm x+2=\frac{ -2 }{ 5 }y\] to get rid of the fraction at right side what would u do ? remember it's -2 divided by 5
Nnesha
  • Nnesha
nd ofc y
Adi3
  • Adi3
2/5 = 2.5
Adi3
  • Adi3
-2.5
Adi3
  • Adi3
@imqwerty -2.5
Nnesha
  • Nnesha
well i'm pretty sure they aren't looking for decimal answer
Adi3
  • Adi3
yup
Nnesha
  • Nnesha
\[\huge\rm x+2=\frac{ -2 }{ 5 }y\] to get rid of the fraction at right side what would u do ? remember it's -2 divided by 5
Nnesha
  • Nnesha
how would you cancel out 5 from right side ?
Adi3
  • Adi3
multiply
imqwerty
  • imqwerty
no its not -2.5
Nnesha
  • Nnesha
multiply by what ?
Adi3
  • Adi3
ok
Adi3
  • Adi3
they do not want a answer in deci
Adi3
  • Adi3
5 @Nnesha
imqwerty
  • imqwerty
see if u got something like this - \[x \times y\]and u wanna get rid of y then what u do is that just multiplay it by 1/y then u get-\[x \times y \times \frac{ 1 }{ y }\] y and y get cut and u get ur x
Adi3
  • Adi3
the answer is \[5 - \frac{ 5 }{ 2 }x\]
Nnesha
  • Nnesha
yes right multiply both sides by 5 \[\huge\rm 5(x+2)=\frac{ -2 }{ 5 }y \times 5\] always first try to get rid of de fraction
Adi3
  • Adi3
ok
Nnesha
  • Nnesha
can you explain plz how did you get -5 /2 and just 5 ?
Adi3
  • Adi3
that is the answer, thats part i dont get it
Nnesha
  • Nnesha
yes right multiply both sides by 5 \[\huge\rm 5(x+2)=\frac{ -2 }{ 5 }y \times 5\] distribute parentheses by 5 5(x+2) = ???
Adi3
  • Adi3
5x + 10
Adi3
  • Adi3
it is like 11:00 P.M here so i am gonna sleep, bye, cant understand anything right now. bye
Nnesha
  • Nnesha
right \[\huge\rm 5x+10 =-2y\]last step
Nnesha
  • Nnesha
there is only one step ........ -2 ` times ` y so to cancel it out divide by sides by -2
Adi3
  • Adi3
(5x + 10)/2
Nnesha
  • Nnesha
-2 not just 2 and (5x+10)/-2 can be written as 5x/-2 + 10/-2 \[\huge\rm \frac{ 5x+10 }{ -2}=\frac{ 5x }{ -2 }+\frac{ 10 }{ -2}\]now jsut simplify
Adi3
  • Adi3
ok, thank you
Nnesha
  • Nnesha
np

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