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# HELP!

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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)\$?

Mar 18, 2018

### Best Answer

#1
+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

Mar 19, 2018

### 1+0 Answers

#1
+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