Question

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

Answer 1

Hint: In the given question they have given an equation and asked us to find the value of $f\left( { - 3} \right)$. In this type of problem we need to substitute the value they have asked for that is $x = - 3$ in the given equation which is $f(x) = 3x - 5$ and simplify the expression to get the required answer.

Complete step by step answer:
Here in this given question they have asked to find the value of $f\left( { - 3} \right)$ for which they have also given an equation for $f(x)$ given by: $f(x) = 3x - 5$.
From the given function we can notice that we need to find the value of $f\left( { - 3} \right)$ therefore, $x = - 3$. Just by replacing the $x$ term in the given equation that is $f(x) = 3x - 5$ with the value they have asked to find, here it is $ - 3$ we can easily get the answer.
Now substitute the value that is $x = - 3$ in the given equation $f(x) = 3x - 5$ and simplify the expression, to find the value of $f\left( { - 3} \right)$.
Therefore, on substitution we get
$f( - 3) = (3 \times - 3) - 5$
On simplifying the above expression for $f\left( { - 3} \right)$, we get
$ \Rightarrow f( - 3) = - 9 - 5$
$ \Rightarrow f( - 3) = - 9 - 5$
Therefore, we get
$ \Rightarrow f( - 3) = - 14$.

Hence, the value of $f\left( { - 3} \right)$ is $ - 14$ for the given equation $f(x) = 3x - 5$.

Note:
Whenever we have this type of problem, which is finding the value for the particular value of $x$ from the given equation, we can directly substitute the value for $x$ in the given equation and simplifying the expression, we arrive at the required answer. Here the important step is just the simplification part. If you are good at simplifying the expression then you are going to get the correct answer.