Question

How do you find $g\left( f\left( x \right) \right)$ if $g\left( x \right)={{x}^{2}}$ and $f\left( x \right)=x+3$ ?

Answer 1

In this question we have been asked to find the value of $g\left( f\left( x \right) \right)$ for $g\left( x \right)={{x}^{2}}$ and $f\left( x \right)=x+3$ . This can be done by substituting $f\left( x \right)$ in the place of $x$ in the given function $g\left( x \right)={{x}^{2}}$ . By substituting and simplifying we will get the required answer. For simplifying we will perform some simple basic arithmetic calculations to reduce it.

Complete step by step solution:
Now considering from the question we have asked the value of $g\left( f\left( x \right) \right)$ for $g\left( x \right)={{x}^{2}}$and $f\left( x \right)=x+3$ .
For that sake we will substitute $f\left( x \right)$ in the place of $x$ in the given function $g\left( x \right)={{x}^{2}}$ .
By substituting we will have $\Rightarrow g\left( f\left( x \right) \right)=g\left( x+3 \right)$ .
Now we will simplify this expression. After simplifying we will have $\Rightarrow g\left( f\left( x \right) \right)={{\left( x+3 \right)}^{2}}$ .
Therefore we can conclude that the value of $g\left( f\left( x \right) \right)$ for $g\left( x \right)={{x}^{2}}$and $f\left( x \right)=x+3$ is $g\left( f\left( x \right) \right)={{\left( x+3 \right)}^{2}}$ .

Note:
While answering this question we should be sure about the calculations we perform and the concept we apply while answering this question. This is a very simple and easy question, very few mistakes are possible and it can be answered in very less span of time. Similarly we can find the value of $g\left( x \right)$and $f\left( x \right)$ for any value of $x$ simply by substituting and performing some simple basic arithmetic calculations to further simplify and reduce the expression. For example we can find the value of $f\left( g\left( x \right) \right)$ by substituting $g\left( x \right)={{x}^{2}}$ in the expression $f\left( x \right)=x+3$ we will have $\Rightarrow f\left( g\left( x \right) \right)=f\left( {{x}^{2}} \right)$ and for this we will perform simple basic arithmetic calculations to further simplify and after reducing we will have $\Rightarrow f\left( g\left( x \right) \right)={{x}^{2}}+3$ .