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Given that f(x) = 4x + k , and g(x) = x - 2 , find the possible value of m and k if  f[g(x)] = mx + 8

 Jan 16, 2018
 #1
avatar+95872 
+1

Given that f(x) = 4x + k , and g(x) = x - 2 , find the possible value of m and k if  f[g(x)] = mx + 8

 

I'm assuming that these represent linear equations  with m = slope and k  = y intercept

 

f (g (x) )  =   4 (x - 2)  +  k  

 

So.....

 

4(x - 2) +  k  =  mx +  8     

 

4x  -  8  + k  =  mx  +  8            let k  =  16

 

4x  + 8  =  mx  + 8         ⇒      m   =  4

 

 

So

 

m  =  4     and  k   =  16

 

 

cool cool cool

 Jan 16, 2018
 #2
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How do you get k = 16?

Guest Jan 16, 2018
 #3
avatar+95872 
+1

If  -8  +  k  is the y intercept of one line  and  8 is the y intercept of the other....and we want the y intercepts to be the same, we have that

 

-8  +  k  =  8      add 8 to both sides

 

k   =  16

 

 

cool cool cool

 Jan 16, 2018

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