I say yes 1-1 passes the horizontal line test
f(x)= (5) / (3x+7)
Yes note that $\displaystyle f(x)=\frac{5}{3x+7}$ is monotonically decreasing over the reals except at its points of discontinuity so it wont "repeat" itself in terms of values. So it is one-to-one on that interval. Now the inverse would be $\displaystyle \frac{5-7y}{3y}=f^{-1}(y)$