The function [f(x)=(x^2+2 x-15)/(x^2-4 x+9), x R] is

Question

The function $$f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in \mathbb{R}$$ is

Accepted Answer

The function $ f(x)=\frac{x^2+2x-15}{x^2-4x+9}, x \in \mathbb{R} $ can be simplified to $ f(x)=\frac{(x-3)(x+5)}{x^2-4x+9} $.

For $ x=3 $ and $ x=-5 $, $ f(x) $ equals 0. Therefore, $ f(x) $ is not one-one as it yields the same output for different input values.

The range of $ f(x) $ is $ [-2, 1.6] $, indicating that $ f(x) $ does not cover all possible real values. Consequently, $ f(x) $ is not onto.

Thus, the function is neither one-one nor onto.

Solutions · 1