Question

G (x) = 3x + 12 for x = 5

Answer 1

We will investigate how to evaluate a given function as per the indicated value of the independent variable.

A function is defined as a relationship between two variables ( x and y ). One of these variables mostly ( x ) is denoted as an independent quantity and ( y ) as the independent quantity.

A unique mathematical relationship is expressed between the two variables. Where, the independent variable ( x ) serves as an input to the function. The function is then evaluated on the basis of mathematical manipulation to give the output ( y ).

We have a function g ( x ) defined as follows:

`g\text{ ( x ) = 3x + 12}`

We are to evaluate the above function for the indicated value of the input ( independent variable ) - x as follows:

`x\text{ = 5}`

The process of function evaluation always start with the substitution of the indicated value of independent variable ( x ) into the function relation as follows:

`g\text{ ( 5 ) = 3}\cdot(5)\text{ + 12}`

Then we go about applying the basic mathematical operation defined in the relationship expressed. Keeping in mind the order in which each mathematical operator is to be performed i.e PEMDAS rule!

We will go ahead and solve our parenthesis and evaluate the function g ( x ) at x = 5 as follows:

`\begin{gathered} g\text{ ( 5 ) = 15 + 12} \\ g\text{ ( 5 ) = 27} \end{gathered}`

For the indicated value of the independent variable ( x = 5 ) the function g ( x ) outputs the the value of:

`27\ldots\text{ Answer}`