Given the function $f(x)=x^2$
i) Write $f^{-1}(x)$ in the form of $y$
ii) Sketch the graph $f^{-1}(x)$ and $f^{-1}(x+1)$ on the same set of axes
iii) Use your graphs to solve for $x$ if $\log_2(x+2) < 1$
Now looking at the solution, the graph shows that the Inverse function going through the point $(1,0)$ so what i don't understand is that how did they get to the mentioned point if no value of $x$ or $y$ is given (so I could plug $y$ OR $x$ into the equation and and find $x$ & $y$ values in order to sketch the graph?
First of all, in order for an inverse function to be defined you must find if the initial function is 1-1, meaning that $f(x_1)=f(x_2)$ implies $x_1=x_2.$ Once you've checked that you take into account this: The main function and the inverse function happen to have the following property (The proof is very obvious if you consider the meaning of the inverse function): Their axis of symmetry is the line $y=x$. So when trying to sketch its graph you just find the symmetrical line with regard to $f(x)$ having as axis of symmetry the straight line $y=x$.