Question

How do you find \[f\left( { - 3} \right)\] given \[f\left( x \right) = 2x + 2\] ?

Answer 1

Hint: We are given a function \[f\left( x \right)\] and asked how we will find the value of \[f\left( { - 3} \right)\] . Recall the general equation for a polynomial of degree \[n\] and recall the method to find the value of function at a particular value. Use this method to find the value of \[f\left( { - 3} \right)\] .

Complete step-by-step answer:
Given, the function \[f\left( x \right) = 2x + 2\]
We are asked to find the value of \[f\left( { - 3} \right)\] .
The given function is a polynomial function.
If we have a polynomial of degree \[n\] , such that
  \[f\left( x \right) = a{x^n} + b{x^{n - 1}} + c{x^{n - 2}} + .......\]
where \[f\left( x \right)\] is a function of \[x\] .
And we are asked to find the value of \[f\left( {{x_o}} \right)\] then we substitute the value of \[x\] as \[{x_o}\] . That is,
  \[f\left( {{x_o}} \right) = a{x_o}^n + b{x_o}^{n - 1} + c{x_o}^{n - 2} + .......\]
Here, \[f\left( x \right) = 2x + 2\] and \[{x_o} = - 3\] so, substituting \[x\] as \[ - 3\] in the function \[f\left( x \right)\] we get,
  \[f\left( { - 3} \right) = 2 \times \left( { - 3} \right) + 2\]
  \[ \Rightarrow f\left( { - 3} \right) = - 6 + 2\]
  \[ \Rightarrow f\left( { - 3} \right) = - 4\]
Therefore, the value of \[f\left( { - 3} \right)\] is \[ - 4\] .
So, the correct answer is “ \[ - 4\] ”.

Note: A function can be defined as the relationship between a set of inputs and a set of possible outcomes. If we have \[y = f\left( x \right)\] that is, \[y\] is a function of \[x\] then the values of \[x\] are inputs and the values obtained for \[y\] are possible set of outcomes. In the above question \[ - 3\] is the input and \[ - 4\] is the outcome. Polynomial function is a type of function we can express as polynomial.