Question

Range of $f\left(x\right)=({20}^x-20)$ is

• A. $\left(0,\infty \right)$
• B. $\left[-20,\infty \right)$
• C. $\left[-20,20\right]$
• D. $\left(-20,\infty \right)$

Answer 1

The correct option is D $\left(-20,\infty \right)$

$f\left(x\right)={20}^x-20$

$\therefore f^{\prime }\left(x\right)={20}^{x}log20=$ always +ve

$\therefore f\left(x\right)$ is monotonically increasing

function

$\therefore$ min value of f(x) will be at $x\to -\infty$

${\therefore }_{min}^{f\left(n\right)}={20}^{-\infty }-20=-20$

and ${}_{man}^{f\left(x\right)}$ at $x\to \infty =\infty$

$\therefore$ range of $\left(f\right(n\left)\right)=(-20,\infty )$

D correct option