Question

what is the inverse of (7)/3-x

Answer 1

Multiplicative inverse or additive inverse?
Multiplicative inverse would be (3-x)/7

Additive inverse would be -7/(3-x)

Answer 2

I assume you are doing pre-calculus.

The inverse of f(x) = f^-1(x) can be found by the following simple steps:
1. rewrite the function y=f(x) by interchanging x and y.
2. solve the resulting equation for y in terms of x. The resulting expression on the right hand side is f^-1(x).
3. Check your answer by evaluating
f(f^-1(x)). It should be equal to x.

Here are the details:
f(x)=y=7/(3-x)
1. exchange x and y:
x=7/(3-y)
2. Solve for y in terms of x
f^-1(x)=y=3-7/x
3. Check the answer:
f(f^-1(x))
=f(3-7/x)
=7/(3-(3-7/x))
=7/(7/x)
=x
f^-1(x)=y=3-7/x is therefore the inverse of f(x)=7/(3-x).

Answer 3

x+7/3