Given:
[tex]y=f(x)[/tex]
[tex]f(x)=\dfrac{1}{2}x-3[/tex]
To find:
The input when the output is – 3.
Solution:
We have,
[tex]f(x)=\dfrac{1}{2}x-3[/tex]
Substituting [tex]f(x)=y[/tex], we get
[tex]y=\dfrac{1}{2}x-3[/tex] ...(i)
We need to find the input when the output is – 3. It means, we have to find the value of x when [tex]y=-3[/tex].
Putting [tex]y=-3[/tex] in (i), we get
[tex]-3=\dfrac{1}{2}x-3[/tex]
[tex]-3+3=\dfrac{1}{2}x[/tex]
[tex]0=\dfrac{1}{2}x[/tex]
Multiply both sides by 2.
[tex]0=x[/tex]
Therefore, the input is 0 when the output is -3.
