Question

$f$ is a function such that $f\left(x\right)<0$. The graph of a new function $g$ defined by $g\left(x\right)=\left|f\right(x\left)\right|$ is a reflection of the graph of $f$

• A. on the y axis
• B. on the x axis
• C. on the line y=x
• D. on the line y=-x

Answer 1

The correct option is B on the x axis

$f\left(x\right)<0$

$g\left(x\right)=\left|f\left(x\right)\right|=-f\left(x\right)$

$f\left(x\right)\&-f\left(x\right)$ are reflections in x-axis.

$\therefore q$ is reflection of $f$ on x-axis.

From $[\frac{\pi }{2},\pi ]$ both $\sin x\&\cos x$ are decreasing.

let $f\left(x\right)=\sin x$

$f^{\prime }\left(x\right)=\cos x$\quad $[\cos xis-veforx\in (\frac{\pi }{2},\pi )]$

$\therefore f^{\prime }\left(x\right)<0\Rightarrow f\left(x\right)$ is decreasing.

$g\left(x\right)=\cos x$

$g^{\prime }\left(x\right)=-\sin x$ $[-\sin xis-veforx\in (\frac{\pi }{2},\pi )]$

$\therefore g^{\prime }\left(x\right)<0\Rightarrow g\left(x\right)$ is decreasing.