Question

The function $f:(-\infty,-1] \rightarrow\left[e^5, \infty\right)$ defined by $f(x)=e^{x^2-3 x+2}$ is

• A. one one but not onto
• B. onto but not one-one
• C. neither one one nor onto
• D. both one one and onto

Answer 1

Answer: (A)

$f(x)=e^{x^2-3 x+2}$, let $g(x)=x^2-3 x+2$

Clearly g is decreasing in $(-\infty,-1]$ and has range $[6, \infty)$
$\therefore R _{ f }:\left[ e ^6, \infty\right) $
$\therefore f $ is onto & one-one. ]