Given:
The equation is:
[tex]y=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex]
To find:
The function notation for the given equation and then solve the function for the value [tex]x=\dfrac{1}{3}[/tex].
Solution:
We have,
[tex]y=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex]
Substitute [tex]y=f(x)[/tex] in the given equation to find the function notation of it.
[tex]f(x)=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex]
Substituting [tex]x=\dfrac{1}{3}[/tex], we get
[tex]f(\dfrac{1}{3})=-\dfrac{2}{5}(\dfrac{1}{3})+\dfrac{3}{8}[/tex]
[tex]f(\dfrac{1}{3})=-\dfrac{2}{15}+\dfrac{3}{8}[/tex]
[tex]f(\dfrac{1}{3})=\dfrac{-16+45}{120}[/tex]
[tex]f(\dfrac{1}{3})=\dfrac{29}{120}[/tex]
Therefore, the function notation is [tex]f(x)=-\dfrac{2}{5}x+\dfrac{3}{8}[/tex] and the value of the function at [tex]x=\dfrac{1}{3}[/tex] is [tex]\dfrac{29}{120}[/tex].
