Answer to Question #146878 in Discrete Mathematics for Haider

Question

Show graphically that which of the following is one to one function
(1)f(x)=ln(x)
(2)g(x)=e^x
(3) h(x)=x³

Answer 1

If some horizontal line intersects the graph of the function more than once, then the function is not one-to-one. Otherwise, the function is one-to-one.

1) $f(x)=ln(x)$

There is no horizontal line that intersects the graph of the function more than once. Therefore $f(x)=ln(x)$ is one-to-one function.

2) $g(x)=e^x$

There is no horizontal line that intersects the graph of the function more than once. Therefore $g(x)=e^x$ is one-to-one function.

3) $h(x)=x^3$

There is no horizontal line that intersects the graph of the function more than once. Therefore $h(x)=x^3$ is one-to-one function.

Answer: all three functions are one-to-one.