Question

Diagram 1 shows absolute function of f(x)= 3x-1a)State the domain for that functionb)State the value of a

Answer 1

The function given is,

`f(x)=3x-1`

a) Domain

This is the set of all points over which a function is defined.

Therefore, the domain of the function is

`-2\leq x\leq1`

b) Solving for the value of a

To solve for the value of a, the value of y = 0 at x = a

Therefore,

`\begin{gathered} f(x)=3x-1 \\ \text{where,} \\ f(x)=y=0 \\ x=a \end{gathered}`

Solving for a

`\begin{gathered} 0=3(a)-1 \\ 0=3a-1 \\ \end{gathered}`

Collect like terms

`\begin{gathered} 3a=0+1 \\ 3a=1 \end{gathered}`

Divide both sides by 3

`\begin{gathered} (3a)/(3)=(1)/(3) \\ a=(1)/(3) \end{gathered}`

Hence,

`a=(1)/(3)`