Question

Let $f:\left(-\infty ,2\right)\to \left[6,\infty \right).f\left(x\right)=4x^2-16x+22$ and $p\left(x\right)$ is a function such that graph of $f\left(x\right)$ are mirror image of each other $w.r.t$ line $y=x$, then $P\left(10\right)$ will be :-

• A. $2$
• B. $1$
• C. $3$
• D. both (B) & (C)

Answer 1

The correct option is A $2$

$y=4x^2-16x+22$

when it is reflected

about $y=x$

$x=4y^2-16y+22$

$p\left(10\right)\Rightarrow 4y^2-16y+12=0$

$2y^2-8y+6=0$

$y^2-4y+3=0$

$y^2-y-3y+3=0$

$y(y-1)-3(y-1)=0$

$(y-1)(y-3)=0y=1$ or $3$