The function f(x) = x^2+2x-15/x^2-4x+9, x ∈ R is (1) both one-one and onto. (2) onto but not one-one.

Question

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

(1) both one-one and onto. 

(2) onto but not one-one. 

(3) neither one-one nor onto. 

(4) one-one but not onto.

(5) none of these

Answer 1

Correct option is (5) none of these

\(f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}\)

\(f^{\prime}(x)=\frac{\left(x^2-4 x+9\right)(2 x+2)-\left(x^2+2 x-15\right)(2 x-4)}{\left(x^2-4 x+9\right)^2}\)

\(f^{\prime}(x)=\frac{-6 x^2+48 x-42}{\left(x^2-4 x+9\right)^2}\)

So f'(x) is +ve & -ve so many one and into