Question

If $f\left( x \right)=2x+3x+5$, how do you find $3f\left( -2 \right)$?

Answer 1

In this problem we have given a function called $f\left( x \right)$ which is equal to $2x+3x+5$ and they have asked to calculate the value of $3f\left( -2 \right)$. We can write the required value $3f\left( -2 \right)$ as $3\times f\left( -2 \right)$ which is three times of the value of the function at $x=-2$. For this we need to calculate the value of the function at $x=-2$ which is $f\left( -2 \right)$. For this we are going to substitute the value $x=-2$ in the given equation and simplify the equation by using the algebraic formulas to get the value of $f\left( -2 \right)$. After calculating the value of $f\left( -2 \right)$ we will multiply the obtained value with $3$ to get the required value.

Complete step by step answer:
Given function, $f\left( x \right)=2x+3x+5$.
The value of the above function at $x=-2$ will be calculated by substituting $x=-2$ in the above equation, then we will get
$f\left( -2 \right)=2\left( -2 \right)+3\left( -2 \right)+5$
We know that when we multiplied a positive sign with the negative sign, then we will get the negative sign as a result. Then the above equation is modified as
$\Rightarrow f\left( -2 \right)=-2\times 2-3\times 2+5$
Substituting the multiplication values in the above equation, then we will get
$\Rightarrow f\left( -2 \right)=-4-6+5$
Simplifying the above equation by adding the terms which having negative signs and we will put a negative sign to the sum, then the above equation will be
$\Rightarrow f\left( -2 \right)=-10+5$
Subtracting $10$ from $5$ will give $-5$ as a result. Hence the value of $f\left( -2 \right)$ is
$\Rightarrow f\left( -2 \right)=-5$
Now multiplying the above equation with $3$ on both sides, then we will get
$\Rightarrow 3\times f\left( -2 \right)=3\times -5$
Simplifying the above equation, then we will get
$\Rightarrow 3f\left( -2 \right)=-15$

Hence the value of $3f\left( -2 \right)$ where $f\left( x \right)=2x+3x+5$ is $-15$.

Note: For this problem we can simplify the given equation and then we can calculate the required value. If you observe the given equation, we have the terms $2x$, $3x$ in summation. So, we can write the sum of $2x$, $3x$ as $5x$, then the given equation is modified as
$\begin{aligned} & \Rightarrow f\left( x \right)=2x+3x+5 \\\ & \Rightarrow f\left( x \right)=5x+5 \\\ \end{aligned}$
In the above equation taking $5$ as common, then we will get
$f\left( x \right)=5\left( x+1 \right)$
Now we can substitute the value $x=-2$ and calculate the required result.