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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)?

 Jun 10, 2021
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f(x) = 7x + 5

and g(x) = x + 1

 

⇒ \(h(x)=f(g(x))\)

              \(=f(x+1)\)

              \(=7x+7+5\)

              \(=7x+12\)

 

In order to find  \(h^{-1}(x)\) 

Let  \(y=h(x)\)

       \(y=7x+12\)

       \(x= {y-12\over 7}\)

⇒ \(h^{-1}(x) = {x-12 \over 7}\)

 

   Thus, inverse of h(x) is \({x-12 \over 7}\)

 

 

~Amy 

 Jun 10, 2021
edited by amygdaleon305  Jun 10, 2021

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