Given-f-x-2x-m-f-2-x-px-6-Find-the-value-of-m-and-p-

Question Number 106044 by ZiYangLee last updated on 02/Aug/20

Given f (x) = 2 x + m, f^{2} (x) = px + 6

Find the value of m and p .

Answered by 1549442205PVT last updated on 02/Aug/20

f^{2} (x) = {4 x}^{2} + 4 mx + m^{2} .

f^{2} (x) = px + 6 \Leftrightarrow {4 x}^{2} + 4 mx + m^{2} = px + 6

\Rightarrow p = ax + b \Rightarrow {4 x}^{2} + 4 mx + m^{2} = (ax + b) x + 6

\Leftrightarrow {4 x}^{2} + 4 mx + m^{2} = {ax}^{2} + bx + 6

\Rightarrow {\begin{cases} a = 4 \\ 4 m = b \\ m^{2} = 6 \end{cases} \Leftrightarrow {\begin{cases} m = \pm \sqrt{6} \\ b = \pm 4 \sqrt{6} \\ a = 4 \end{cases}

Thus, p = 4 x \pm 4 \sqrt{6}, m = \pm \sqrt{6}

Commented by ZiYangLee last updated on 03/Aug/20

thanks < 3