Question

The range of the function $f\left(x\right)=\frac{e^{x}Inx{5}^{(}{x}^2+2\left)\right(x^2-7x+10)}{2x^2-11x+12}$ is

• A. $(-\infty ,\infty )$
• B. $[0,\infty )$
• C. $(\frac{3}{2},\infty )$
• D. $(\frac{3}{2},4)$

Answer 1

The correct option is A $(-\infty ,\infty )$

$f\left(x\right)=\frac{e^{x}lnx(x^2+2)(x^2-5x-2x+10)}{{2x}^2-8x-3x+12}$

$=\frac{e^{x}lnx(x^2+2)(x-2)(x-5)}{(2x-3)(x-4)}$

$\because domain=R-\{\frac{3}{2},4\}.$

But $f\left(x\right)$ in defend for all value of $x$ as per the group of $f\left(x\right).$

Hence Range of $f\left(x\right)=(-\infty ,\infty ).$