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

Question

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

Accepted Answer

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