## Calculus: Early Transcendentals 8th Edition

(a) One to one function is the mapping such that $$f(x_1)=f(x_2)\Rightarrow x_1=x_2.$$ If the arbitrary horizontal line intersects the graph of the function once at most then the function is one-to-one. (b) $$f(x)=y\Rightarrow x=f^{-1}(y).$$ We obtain the graph of $f^{-1}$ by reflecting the graph of $f$ about the line $y=x$.
(a) One to one function is the mapping such that only one element of the domain $x$ maps to a certain element $y$ of the range i.e. $$f(x_1)=f(x_2)\Rightarrow x_1=x_2.$$ To tell from the graph ve can use the horizontal line test. If arbitrary horizontal line intersects the graph of the function once at most then the function is one-to-one since then only one value of $x$ corresponds to the certain value of $y$. (b) If the element $x$ of the domain maps by $f$ to $y$ then $y$ maps to $x$ by $f^{-1}$ i.e. $$f(x)=y\Rightarrow x=f^{-1}(y).$$ We obtain the graph of $f^{-1}$ by reflecting the graph of $f$ about the line $y=x$.