$\left(\begin{matrix}\\ \frac{ 1}{ x-1 }\end{matrix}\right) + 3$

$\frac{ 1 }{ x-1} + 3$

if this more clear

4. 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

ok, x - 3 = $\frac{ 1 }{ y-1 }$

is that right

@IrishBoy123

@HELPMEPLZ!!

still on inverse, this is too much for me

10. 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 ?

divde it?

12. imqwerty

write y in terms of x and then jst switch y and x :) function which u get is inverse

13. Nnesha

its already divided by 1 (1/y-1 )to cancel it out you should do opposite of division

multiply

15. Nnesha

yes right multiply both sides by y-1

so 1x-3

17. 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

ohh, then how to get y by itself?

19. Nnesha

how would you cancel x-3 from left side ?

divide

21. Nnesha

right so divide both sides by x-3 let me know what you get

22. Nnesha

it's multiplication( y-1 ) times (x-3) so yes you should divide

y-1 = 1/x-3

24. Nnesha

right whats nexxt ?

y = 1/x-3 + 1

26. Nnesha

right now we should get the common denominator |dw:1443366122753:dw|

OK, Can i ask a last question

pls

29. imqwerty

yea y nt :)

30. Nnesha

yes ?

ok, thank you all. find the inverse of $-\frac{ 2 }{ 5}x - 2$

g(x) =

33. Nnesha

same steps try it first

x+2 = -2/5y

35. imqwerty

yea nxt

thts wht idk

37. imqwerty

think a way to isolate y

38. Nnesha

now $x+2 =\frac{ -2 }{ 5 }y$ what would be the nexxt step ?

divide?

40. imqwerty

divide by what..

41. Nnesha

right divide what ?

idk

-2/5

44. Nnesha

well first you need to get rid of the fraction

45. imqwerty

if u have 2x and u want just x then what number will u divide it by?

46. 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

47. Nnesha

nd ofc y

2/5 = 2.5

-2.5

@imqwerty -2.5

51. Nnesha

well i'm pretty sure they aren't looking for decimal answer

yup

53. 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

54. Nnesha

how would you cancel out 5 from right side ?

multiply

56. imqwerty

no its not -2.5

57. Nnesha

multiply by what ?

ok

they do not want a answer in deci

5 @Nnesha

61. 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

the answer is $5 - \frac{ 5 }{ 2 }x$

63. 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

ok

65. Nnesha

can you explain plz how did you get -5 /2 and just 5 ?

that is the answer, thats part i dont get it

67. 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) = ???

5x + 10

it is like 11:00 P.M here so i am gonna sleep, bye, cant understand anything right now. bye

70. Nnesha

right $\huge\rm 5x+10 =-2y$last step

71. Nnesha

there is only one step ........ -2  times  y so to cancel it out divide by sides by -2

(5x + 10)/2

73. 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

ok, thank you

75. Nnesha

np