+0  
 
0
42
2
avatar+272 

 Let f(x) = 2x + 7 and g(x) = 3x + c. Find c if (f @ g)(x) = (g @ f)(x) for all x.

 

Thanks :D

WhichWitchIsWhich  Nov 6, 2017

Best Answer 

 #1
avatar+5258 
+1

f(x)  =  2x + 7

g(x)  =  3x + c

 

f( g(x) )  =  f( 3x + c )  =  2( 3x + c ) + 7

 

g( f(x) )  =  g( 2x + 7 )  =  3( 2x + 7 ) + c

 

And we want to know what  c  is when  f( g(x)  )  =  g( f(x) )  . That is... when

 

2( 3x + c ) + 7  =  3( 2x + 7 ) + c           Distribute the numbers outside the parenthesees.

 

6x + 2c + 7  =  6x + 21 + c                   Subtract  6x  from both sides of the equation.

 

2c + 7  =  21 + c             Subtract  c  from both sides of the equation.

 

c  + 7  =  21                    Subtract  7  from both sides of the equation.

 

c  =  14

hectictar  Nov 6, 2017
Sort: 

2+0 Answers

 #1
avatar+5258 
+1
Best Answer

f(x)  =  2x + 7

g(x)  =  3x + c

 

f( g(x) )  =  f( 3x + c )  =  2( 3x + c ) + 7

 

g( f(x) )  =  g( 2x + 7 )  =  3( 2x + 7 ) + c

 

And we want to know what  c  is when  f( g(x)  )  =  g( f(x) )  . That is... when

 

2( 3x + c ) + 7  =  3( 2x + 7 ) + c           Distribute the numbers outside the parenthesees.

 

6x + 2c + 7  =  6x + 21 + c                   Subtract  6x  from both sides of the equation.

 

2c + 7  =  21 + c             Subtract  c  from both sides of the equation.

 

c  + 7  =  21                    Subtract  7  from both sides of the equation.

 

c  =  14

hectictar  Nov 6, 2017
 #2
avatar+78756 
+1

This is an interesting problem......thanks, hectictar......!!!!

 

cool cool cool

CPhill  Nov 6, 2017

10 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details