Question

The minimum value of $f\left(x\right)=|3-x|+7$ is

• A. $0$
• B. $6$
• C. $7$
• D. $8$
• E. $10$

Answer 1

The correct option is C

$7$

Find the minimum value of the given function

Given : $f\left(x\right)=|3-x|+7$

$f\left(x\right)=\left\{\begin{array}{ll}\left(3-x\right)+7,& 3-x\ge 0\\ -\left(3-x\right)+7,& 3-x<0\end{array}\right.$

$f\left(x\right)=\left\{\begin{array}{ll}10-x,& 3\ge x\\ 4+x,& 3<x\end{array}\right.$

$$\begin{gathered} f\left(1\right)>f\left(2\right)>f\left(3\right)<f\left(4\right)<f\left(5\right)........ \\ \Rightarrow 9>8>7<8<9<..... \end{gathered}$$

Here, at $x=3,f\left(x\right)=7$

Therefore, the minimum value of $f\left(x\right)=7$.

Hence option $\left(C\right)$ is the correct answer.