Question

If $f\left( x \right) = 3x - 1$ and $g\left( x \right) = 4x + 2$, what is the value of $g\left( {f\left( 0 \right) + 2} \right)$ ?

Answer 1

Hint: In the given question, we are provided with the expressions of two functions and we have to find the value of expression $g\left( {f\left( 0 \right) + 2} \right)$.So, we first find the value of function $f\left( x \right)$ with value of x as zero, then we substitute the value of $f\left( 0 \right)$ in the required expression and find the final answer. This question requires us to have the knowledge of basic and simple algebraic rules and operations such as substitution, addition, multiplication, subtraction and many more like these.

Complete step by step answer:
In the given question, we are given the functions $f\left( x \right) = 3x - 1$ and $g\left( x \right) = 4x + 2$.Now, we have to find the value of the expression $g\left( {f\left( 0 \right) + 2} \right)$. So, we first find the value of $f\left( 0 \right)$ by substituting the value of $x$ as zero in $f\left( x \right) = 3x - 1$.
$f\left( 0 \right) = 3\left( 0 \right) - 1 = 0 - 1 = - 1$

Now, we substitute this value in the expression. So, we get,
$g\left( {f\left( 0 \right) + 2} \right) = g\left( { - 1 + 2} \right)$
$ \Rightarrow g\left( 1 \right)$
So, we have to evaluate the value of $g\left( 1 \right)$. So, substituting the value if x as one in $g\left( x \right) = 4x + 2$, we get,
$ \Rightarrow g\left( x \right) = 4\left( 1 \right) + 2$
$ \therefore g\left( x \right) = 6$

Therefore, the value of $g\left( {f\left( 0 \right) + 2} \right)$ is $6$.

Note: Such questions that require just a 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.