Question

Write each equation in function notation, then solve the function for the given value.

Answer 1

Given:

The equation is:

$y=-\dfrac{2}{5}x+\dfrac{3}{8}$

To find:

The function notation for the given equation and then solve the function for the value $x=\dfrac{1}{3}$.

Solution:

We have,

$y=-\dfrac{2}{5}x+\dfrac{3}{8}$

Substitute $y=f(x)$ in the given equation to find the function notation of it.

$f(x)=-\dfrac{2}{5}x+\dfrac{3}{8}$

Substituting $x=\dfrac{1}{3}$, we get

$f(\dfrac{1}{3})=-\dfrac{2}{5}(\dfrac{1}{3})+\dfrac{3}{8}$

$f(\dfrac{1}{3})=-\dfrac{2}{15}+\dfrac{3}{8}$

$f(\dfrac{1}{3})=\dfrac{-16+45}{120}$

$f(\dfrac{1}{3})=\dfrac{29}{120}$

Therefore, the function notation is $f(x)=-\dfrac{2}{5}x+\dfrac{3}{8}$ and the value of the function at $x=\dfrac{1}{3}$ is $\dfrac{29}{120}$.