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Let $f(x)=7x+5$ and $g(x)=x-1$. If $h(x)=f(g(x))$, then what is the inverse of $h(x)$? Anwer is not [x+5]/6!

 Jul 22, 2018
 #1
avatar+99659 
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f(x) = 7x + 5

g(x) = x - 1

f(g(x))  = 7 (x - 1) + 5  =  7x - 7 + 5 =  7x - 2  =  h(x)

 

So...for h(x)  write  y

 

y = 7x  - 2     add 2 to both sides

 

y + 2 =  7x      dicvide both sides by 7

 

(y + 2)  / 7   = x       "swap" x and y

 

(x + 2)/ 7   = y      for y , write h-1(x)

 

So

 

h-1 ( x)  = (x + 2) / 7

 

 

cool cool cool

 Jul 23, 2018

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