Question

For $f\left( x \right)=-4x$ how do you find $f\left( -1 \right)$ ?

Answer 1

It is given that for any value of x the function is defined by, $f\left( x \right)=-4x$ . Finding $f\left( -1 \right)$ means find the solution of the function for which the value of x is given which is $-1$. Therefore substitute the value of x which is $-1$ in the function, and then evaluate. The result which we are going to get will be $f\left( -1 \right)$.

Complete step by step solution:
The given expression or function is $f\left( x \right)=-4x$
This function means that for any value of x belonging to a real number, the function defined is $f\left( x \right)=-4x$.
Here a function also says that every input x that we give has exactly one output.
In the question, they have asked us to find $f\left( -1 \right)$
So here the value of x is given. It is $-1$ .
Hence to find $f\left( -1 \right)$ we shall substitute the value of x which is $-1$ in the function.
On substituting the value in the given function, we get,
$\Rightarrow f\left( -1 \right)=-4(-1)$
Which on evaluating we get,
$\Rightarrow f\left( -1 \right)=+4$

Hence given that the function, $f\left( x \right)=-4x$ then $f\left( -1 \right)$ is equal to $4$ .

Note: The function defines a property or a relation between the input and the output such that each input relates to exactly one output. This means that if the object $x$ is in the set of inputs (called the domain) then a function $f$ will map the object $x$ to exactly one object $f\left( x \right)$ in the set of possible outputs (called the codomain). One should be careful while substituting the values in the expression. Whenever a function $f(x)$ is given and we have to find the value of $f(p)$, just substitute the value of $p$in place of $x$in the function to get $f(p)$.