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The graphs of a function f(x)=3x+b and its inverse function f^{-1}(x) intersect at the point (-3,a). Given that b and a are both integers, what is the value of a?

 

Please i need quick help thanks :D

 
WhichWitchIsWhich  Nov 10, 2017

Best Answer 

 #2
avatar+17653 
+2

The function  f(x)  =  3x + b  can be written as  y  =  3x + b.

To find the inverse of this function:

1)  interchange the x and y terms:  x  =  3y + b

2)  solve for y:                            x - b  =  3y     --->     3y  =  x - b     --->     y  =  (x - b) / 3

 

To find where they intersect, set the two functions equal to each other:  3x + b  =  (x - b) / 3

and, since they intersect at the point (-3, a), replace x by -3:               3(-3) + b  =  (-3 - b) / 3

                                                                                                                  -9 + b  =  (-3 - b) / 3

                                                                                                              -27 + 3b  =  -3 - b

                                                                                                                       4b  =  24

                                                                                                                         b  =  6

 

So, the original function is  y  =  3x + 6  while the inverse is  y  =  (x - 6) / 3

 

Replace the x in either function with -3 and you get that y = -3, so  a = -3.

 
geno3141  Nov 10, 2017
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2+0 Answers

 #1
avatar+237 
+1

well the way it is described, the lines are locked to intersect along the y axis, so they can't intersect at anything with an x value that is not equal to 0, so there is no solution.

 
OfficialBubbleTanks  Nov 10, 2017
 #2
avatar+17653 
+2
Best Answer

The function  f(x)  =  3x + b  can be written as  y  =  3x + b.

To find the inverse of this function:

1)  interchange the x and y terms:  x  =  3y + b

2)  solve for y:                            x - b  =  3y     --->     3y  =  x - b     --->     y  =  (x - b) / 3

 

To find where they intersect, set the two functions equal to each other:  3x + b  =  (x - b) / 3

and, since they intersect at the point (-3, a), replace x by -3:               3(-3) + b  =  (-3 - b) / 3

                                                                                                                  -9 + b  =  (-3 - b) / 3

                                                                                                              -27 + 3b  =  -3 - b

                                                                                                                       4b  =  24

                                                                                                                         b  =  6

 

So, the original function is  y  =  3x + 6  while the inverse is  y  =  (x - 6) / 3

 

Replace the x in either function with -3 and you get that y = -3, so  a = -3.

 
geno3141  Nov 10, 2017

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