Question

How do you find $f\left( 6 \right)$ given $f\left( x \right) = - \dfrac{2}{3}{x^2} - x + 5$ ?

Answer 1

In this question, we have to find the particular value of the function from the given particular function.
First, we need to observe the given function and according to the definition of the function y, denoted by $y = f\left( x \right)$ where the elements x is the argument or input of the function and y is the value of the function or output or the image of x by f. Putting the given particular value of function replacing x in the function f, we can find out the value of the given particular.

Complete step by step solution:
It is given that, $f\left( x \right) = - \dfrac{2}{3}{x^2} - x + 5$.
We need to find out the exact value of $f\left( 6 \right)$ using the given function.
For doing that, we need to replace the value $6$ as x in $f\left( x \right)$ .
Therefore, we have, $f\left( x \right) = - \dfrac{2}{3}{x^2} - x + 5$ .
Thus, substituting the value $6$ as x in $f\left( x \right)$ , we get,
$f\left( 6 \right) = - \dfrac{2}{3} \times {\left( 6 \right)^2} - 6 + 5$
Solving we get,
$f\left( 6 \right) = - \dfrac{2}{3} \times 36 - 6 + 5$
$f\left( 6 \right) = - \left( {2 \times 12} \right) - 6 + 5$
Hence, $f\left( 6 \right) = - 24 - 6 + 5 = - 25$ .
Therefore, the value of $f\left( 6 \right)$ is $- 25$ .

Note: Function:
A function $f:X \to Y$ is a process or a relation that associates each element of x of a set X, the domain of the function to a single element y of another set Y (possibly the same set), the codomain of the function.
If the function is called f, this relation is denoted by $y = f\left( x \right)$ where the elements x is the argument or input of the function and y is the value of the function or output or the image of x by f.
Tips to find a function for a given value:
To solve a function for a given value, plug that value into the function and simplify it.