Explanation:
I suspect you made a number of typos here.
but what you gave us is (emphasized by the introduction of a few blanks)
g(x) = x - 10/7
remember the priorities of assortment operations :
1. brackets (you did not write any)
2. exponents (you did not give us any indication that there is an exponent involved)
3. multiplications and divisions
4. additions and subtractions
therefore, what you wrote has to be interpreted as mentioned above.
and I suspect you need the inverse function (and not 1/g(x)).
to get an inverse function keep in mind that
"g(x) =" (or any other function letter) stands for "y =".
so, we actually have
y = x - 10/7
and for the inverse function we try to transform this equation into a form of x = ...
then we rename x to y and y to x to create a "normal" function. and that's it.
so,
y = x - 10/7
x = y + 10/7
and therefore, the inverse function is
g¯¹(x) = x + 10/7
now, what if your original function was actually e.g.
g(x) = (x - 10)/7
then
y = (x - 10)/7
7y = x - 10
x = 7y + 10
g¯¹(x) = 7x + 10
what if it was
g(x) = x^(-10/7) = 1/x^(10/7)
y = 1/x^(10/7)
x^(10/7) = 1/y
x¹⁰ = (1/y)⁷ = 1/y⁷
x = (1/y⁷)^(1/10) = 1/y^(7/10)
g¯¹(x) = 1/x^(7/10)
and so on.
did I cover the actual function in your question ?
or was reality even different to these 3 attempts ?