Question

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

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

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. ]