27 Determine whether the following functions are onetoone Ex

27 Determine whether the following functions are one-to-one. Explain

Solution

(a) Function is Not One-to-One.

From the graph of the function we can see that it will pass the Vertical line test, that is, at any point of the graph the vertical line will intersect the curve only once.

But the function does not pass the Horizontal line test, as at y=2 a horizontal line will intersect the curve at two distinct points.

Hence the function is not One-to-One.

(b) Function is One-to-One.

From the graph we can see that a vertical line as well as a horizontal line at any point of the curve will intersect the curve only once. hence the graph satisfy both horizontal and vertical line tests.

hence the given function is One-to-One.