Question

Is it one to one or onto? why?​

Answer 1

Explanation:

Given quadratic function is,

f(x) = -x² - x + 1

Range of the function has been defined as (-∞,
`(5)/(4)` ]

Domain of the function is a set of all real numbers.

From the graph of this function,

At x = -3 and x = 2, value of y = -5

But for one to one functions, every x value should map to a different value of y.

Therefore, function is not one to one.

Since, every value of domain (x-value) maps the range (y-value) in the given range (-∞,
`(5)/(4)` ], function will be defined as onto.

Therefore, this function is ONTO, but NOT ONE TO ONE.