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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 $h(x)$?

Guest Mar 18, 2018

Best Answer 

 #1
avatar+6949 
+2

f(x)  =  7x + 5

g(x)  =  x - 1

 

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

 

h(x)  =  7x - 2

                            To find the inverse, let's replace  h(x)  with  y .

y  =  7x - 2

                            Solve for  x  ....add  2  to both sides of the equation.

y + 2  =  7x

                            Divide both sides by  7 .

(y + 2)/7  =  x

 

x  =  (y + 2)/7      So the inverse of  h(x)  is..

 

h-1(x)  =  (x + 2)/7

hectictar  Mar 19, 2018
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1+0 Answers

 #1
avatar+6949 
+2
Best Answer

f(x)  =  7x + 5

g(x)  =  x - 1

 

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

 

h(x)  =  7x - 2

                            To find the inverse, let's replace  h(x)  with  y .

y  =  7x - 2

                            Solve for  x  ....add  2  to both sides of the equation.

y + 2  =  7x

                            Divide both sides by  7 .

(y + 2)/7  =  x

 

x  =  (y + 2)/7      So the inverse of  h(x)  is..

 

h-1(x)  =  (x + 2)/7

hectictar  Mar 19, 2018

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