Question 735552
Generally we switch the roles of {{{x}}} and {{{y}}} to find the inverse.


1. {(18, -3), (-13, -10), (-3, 17), (0, -15)}

 the inverse:{(-3, 18), (-10, -13), (17, -3), (-15, 0)}

2. {(5, -11), (-19, -19), (-6, -4), (-3, 8), (-12, 5)}

 the inverse:{(-11, 5), (-19, -19), (-4, -6), (8, -3), (5, -12)}

3. {(-9, -8), (-16, 5), (17, 6), (19, 4), (-8, 9), (-10, -10)}

the inverse:{(-8, -9), (6, -16), (6, 17), (4, 19), (9, -8), (-10, -10)}
 

4. {(8, -5), (-4, -14), (16, 12), (-13, 4), (-17, -2), (3, -13)}

 the inverse:{(-5, 8), (-14, -4), (12, 16), (4, -13), (-2, -17), (-13, 3)}

5. {(-14, -9), (-0, 2), (8, -4), (-5, 6), (-7, -4)}

  the inverse:{(-9, -14), (2, 0), (-4, 8), (6, -5), (-4, -7)}

6. {(-15, -1), (0, -1), (-6, -1), (-16, 3)}

the inverse: {(-1, -15), (-1, 0), (-1, -6), (3, -16)}


  7. {{{g(x) = (4/3)x - 7/3}}}....{{{g(x) =y}}}

{{{y = (4/3)x - 7/3}}}

we write {{{x= (4/3)y - 7/3}}} and solve for {{{y}}}

{{{x+7/3= (4/3)y }}}

{{{(x+7/3)/(4/3)= y }}}

{{{3(x+7/3)/4= y }}}

{{{(3x+(7*3)/3)/4= y }}}

  {{{y =(1/4)(3x+7)}}}


8. {{{h(x) = (18x + 2)/10}}}...{{{g(x) =y}}}

 {{{y = (18x + 2)/10}}}..switch {{{x}}} and {{{y}}}

 {{{x = (18y + 2)/10}}}...solve for {{{y}}}

{{{10x = 18y + 2}}}

{{{10x -2= 18y }}}

{{{10x/18 -2/18= y }}}

{{{(5/9)x -1/9= y }}}

{{{(1/9)(5x -1)= y }}}




9. {{{f(x) = (2/9)x - 1/9}}}

 or {{{y = (2/9)x - 1/9}}}....switch {{{x}}} and {{{y}}}

 {{{x= (2/9)y - 1/9}}}

{{{x+1/9= (2/9)y }}}

{{{(x+1/9)/(2/9)=y }}}

{{{9(x+1/9)/2=y }}}

{{{(9x+9/9)/2=y }}}

{{{(9x+1)/2=y }}}

{{{(1/2)(9x+1)=y }}}



10. {{{f(x) = (-6x + 2)/5}}} or {{{y = (-6x + 2)/5}}}

{{{x = (-6y + 2)/5}}}
 
{{{5x = (-6y + 2)}}}

{{{5x-2 = -6y }}}

{{{5x/-6-2/-6 = y }}}

{{{(-5x+2)/6 = y }}}

{{{(1/6)(-5x+2) = y }}}



11. {{{g(x) = (5/8)x - 3/4}}}

 {{{y = (5/8)x - 3/4}}}


 {{{x = (5/8)y - 3/4}}}


 {{{x +3/4= (5/8)y }}}


 {{{(x +3/4)/(5/8)= y }}}


 {{{8(x +3/4)/5= y }}}


 {{{(8x +24/4)/5= y }}}


 {{{(8x +6)/5= y }}}


{{{(1/5)(8x +6)= y }}}




12. {{{h(x) = (8x + 9)/8}}}

 {{{y = (8x + 9)/8}}}

 {{{x = (8y + 9)/8}}}

 {{{8x = 8y + 9}}}

{{{8x-9 = 8y }}}

{{{8x/8-9/8 = y }}}

{{{(1/8)(8x-9) = y }}}


13. {{{h(x) = (-7/5)x - 1}}}

 {{{y = (-7/5)x - 1}}}

 {{{x = (-7/5)y - 1}}}

 {{{x +1= (-7/5)y }}}

 {{{(x +1)/(-7/5)=y }}}

 {{{5(x +1)/-7=y }}}

 {{{-5(x +1)/7=y }}}

 {{{(-5/7)(x +1)=y }}}



14. {{{f(x) = (9/8)x + 3/8}}}

  {{{y = (9/8)x + 3/8}}}

{{{x = (9/8)y + 3/8}}}

{{{x-3/8 = (9/8)y }}}

{{{(x-3/8)/(9/8)=y }}}

{{{8(x-3/8)/9=y }}}

{{{(8x-(3*8)/8)/9=y }}}

{{{(8x-3)/9=y }}}

{{{(1/9)(8x-3)=y }}}



15. {{{g(x) = (18x + -36)/30}}}

 
{{{y = (18x + -36)/30}}}

{{{x = (18y + -36)/30}}}

{{{30x = 18y + -36}}}
 
{{{30x +36= 18y }}}

{{{5x/3 +6/3= y }}}

{{{(1/3)(5x +6)= y }}}



Are {{{f}}} and {{{g }}}inverses of each other? Give your explanation to support your response.

16.  {{{f(x) = (2x -6)/7}}} to make sure if {{{f}}} and {{{g }}}inverses , find inverse of {{{f}}} and see if it is equal to {{{g}}}

or should be {{{f^1=g}}} or {{{g^1=f}}}

{{{y = (2x-6)/7}}}

{{{x = (2y-6)/7}}}

{{{7x = 2y -6}}}

{{{7x+6 = 2y}}}

{{{(7/2)x+6/2 = y}}}

{{{(7/2)x+3 = y}}}...this is {{{f^1}}} and as you can see it is equal  to

       {{{g(x) = (7/2)x + 3}}}
 
do same with  {{{g(x) = (7/2)x + 3}}}

 {{{y = (7/2)x + 3}}}

 {{{x = (7/2)y + 3}}}

{{{x-3 = (7/2)y }}}

{{{(x-3)/(7/2)=y }}}

{{{2(x-3)/7=y }}}

{{{(2x-6)/7=y }}}  .......{{{g}}} is equal  to {{{f^-1}}}
  

so, {{{f}}} and {{{g }}} are inverses of each other


I am sure you will be able to do 17,17, and 19 by yourself


17.  {{{f(x) = -(1/5)x + 3/5}}}
       {{{g(x) = -5x + 3 }}} 
 

18. {{{f(x) = x + 1/2}}}
     {{{g(x) = 1x - 1/2}}}


19. {{{f(x) = (63x + 42)/49}}}
     {{{g(x) = (7/9)x - 2/5}}}

 

20. Fahrenheit and Kelvin temperature scales are related by the formula K = 5/9 (F - 32) + 273. Solve this equation for F.

{{{ K = (5/9) (F - 32) + 273}}}... Solve this equation for {{{F}}}.

{{{ (K-273) = (5/9) (F - 32)}}}


{{{ (K-273)/(5/9) =(F - 32)}}}


{{{ 9(K-273)/5 =F - 32}}}


{{{ 9(K-273)/5+32 =F }}}