Question

How do you evaluate a function$f\left( x \right)=x+7$ for a specific value$f\left( -1 \right)$?

Answer 1

Function in mathematics is a rule by which each element of set A is associated with element of set B. It is a law which defines a relation between the independent variable (one variable) and dependent variable (one variable). A function relates inputs to outputs means a function is a machine in which we input something that gives us output , it is a relation where every input has exactly one output. A function is a relation between the domain and range such that value in the domain corresponds to only one value in the range.

Complete step by step solution:
When evaluating function notation the number in place of $x$ in$f\left( x \right)$ is the number that you plug into$x$ of your given function. In the given question the value of $x$ given is $\left( -1 \right)$.
Put this value of $x=-1$in the given equation$f\left( x \right)=x+7$,we get
So, if $f\left( x \right)=x+7$ then $f\left( -1 \right)$ is
$\begin{aligned} & \Rightarrow f\left( -1 \right)=\left( -1 \right)+7 \\\ & \Rightarrow f\left( -1 \right)=6 \\\ \end{aligned}$

Hence we get the value of $x=-1$is$f\left( -1 \right)=6$

Note: We can also check that the above answer is correct or not.
Now what we will do, we will put this value of $x=-1$ which is$6$ equals to the given equation$f\left( x \right)=x+7$,we get
$\begin{aligned} & \Rightarrow f\left( x \right)=x+7=6 \\\ & \\\ \end{aligned}$
Now subtract $-7$ from both side of equation, we get
$\begin{aligned} & \Rightarrow x+7-7=6-7 \\\ & \Rightarrow x=-1 \\\ \end{aligned}$
Here we get $x=-1$ which is given in the question. It means our answer is absolutely correct. In the given question $f\left( -1 \right)$ does mean to inverse the out i.e. (–x-7). Thinking about the notations when solving an equation can lead to mistakes because functions have different notations. $f\left( 2 \right)$ does not imply that function is multiplied by 2.