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Let f(x)=3x+4 and g(x)=2x-3. If h(x)=f(g(x)), then what is the inverse of h(x)?

Lightning  Jul 21, 2018
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Let f(x)=3x+4 and g(x)=2x-3. If h(x)=f(g(x)), then what is the inverse of h(x)?

 

f(g(x))  means to put the function g  into  f

 

h(x)  = f(g(x))  = 3 [ 2x - 3 ]  + 4   =   6x - 9 + 4  =  6x - 5

 

So

 

h(x)  = 6x  - 5      for  h(x), write y

 

y  = 6x  - 5        we want to get x by itself...add 5 to both sides

 

y + 5  = 6x       divide both sides by  6

 

[ y + 5 ] / 6    = x         "swap" x and y

 

[ x + 5 ] / 6  = y      and this is the inverse of  h

 

 

cool cool cool

CPhill  Jul 21, 2018

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