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# Inverse function

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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