Question

how to do the 1st question (part b c d are all basically same so please explain those to so i understand)

Answer 1

Given:

`f(x)=x^2-4x+3`

Factorizing the function;

`\begin{gathered} x^2-4x+3=x^2-3x-x+3 \\ =x(x-3)-1(x-3) \\ =(x-1)(x-3) \end{gathered}`

Hence,

`\begin{gathered} x^2-4x+3\leq0 \\ (x-1)(x-3)\leq0 \end{gathered}`

To get the solution, it must satisfy the condition of the inequality given.

`ab\leq0,\text{ }a\ge0,b\leq0`

Hence,

`\begin{gathered} (x-1)(x-3)\leq0 \\ x-1\ge0,x-3\leq0 \\ x\ge1,x\leq3 \\ \\ Combining\text{ the two inequalities, the solution is;} \\ 1\leq x\leq3 \end{gathered}`