Question 1062663
The inverse of g uses the range of g as the domain so, using g, find the x value corresponding to the y value of 1, y=-7, so,
{{{g^(-1)(1)=-7}}}
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To find the inverse of h, use x,y nomenclature,
{{{y=3x-14}}}
Interchange x and y and solve for y. 
This new y is the inverse.
{{{x=3y-14}}}
{{{3y=x+14}}}
{{{y=(x+14)/3}}}
{{{h^(-1)(x)=(x+14)/3}}}
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The composition of a function and its inverse yields the original input.
{{{h^(-1)(h(x))=x}}}
So then,
{{{h^(-1)(h(7))=7}}}
or
{{{3((x+14)/3)-14=(x+14)-14=x}}}