Question

If $f\left( x \right) = x + 3$ and $g\left( x \right) = 2x - 7$, then what is $fog\left( x \right)$ ?

Answer 1

Hint: In the given question, we are required to find the composite function provided by two individual functions.
A composite function is generally a function that is written inside another function. Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”.

Complete step-by-step answer:
In the given question, we are given functions $f\left( x \right) = x + 3$ and $g\left( x \right) = 2x - 7$.
Now, we have to find a composite function $fog\left( x \right)$ using the given original functions.
The composite function to be calculated is $fog\left( x \right)$.
So, we have to change the value of the variable in the original function in order to find the composite function.
Now, we know that,
$ \Rightarrow fog\left( x \right) = f\left[ {g\left( x \right)} \right]$
So, to evaluate the composite function $fog\left( x \right)$, we substitute the value of $g\left( x \right)$ as $2x - 7$ into the function $f\left( x \right) = x + 3$ as variable x. Hence, we get,
$ \Rightarrow fog\left( x \right) = f\left[ {2x - 7} \right]$
$ \Rightarrow fog\left( x \right) = \left( {2x - 7} \right) + 3$
Opening the bracket ad simplifying the calculations, we get,
$ \Rightarrow fog\left( x \right) = 2x - 4$
So, the composite function $fog\left( x \right)$ is equivalent to $2x - 4$.
So, the correct answer is “$2x - 4$”.

Note: Such questions that require just simple change of variable can be solved easily by keeping in mind the algebraic rules such as substitution and transposition. Substitution of a variable involves putting a certain value in place of the variable. That specified value may be a certain number or even any other variable.