How do you find \[h\left( 6 \right)\] given \[h\left( t \right)=\left| t+2 \right|+3\]?

Hint: In this problem, we have to find \[h\left( 6 \right)\], from the given expression \[h\left( t \right)=\left| t+2 \right|+3\]. We can see that the given expression has an absolute function, which eliminates the negative sign. But here we have only positive numbers to be substituted. We can just substitute the number 6 in the given expression in the place of t, i.e. we should replace 6 in the place of t. We can then simplify the steps to get the value of the given function.

Complete step by step answer:
We know that the given expression is,
\[\Rightarrow h\left( t \right)=\left| t+2 \right|+3\]……. (1)
We know that we have to find \[h\left( 6 \right)\].
We can now substitute t=6 in the given expression, we get
\[\Rightarrow h\left( 6 \right)=\left| 6+2 \right|+3\]
We can now simplify the above step, we get
\[\Rightarrow h\left( 6 \right)=\left| 8 \right|+3=11\]
Here we can see that the value inside the absolute brackets is positive so we can directly simplify without any changes to get the answer.

Therefore, the value of \[h\left( 6 \right)=11\].

Note: Students make mistakes, in case we are given a negative number, where we have absolute value or modulus of a real number gives only positive numbers. We should know that, if we are given \[h\left( -6 \right)\], then the answer would be,
\[\Rightarrow h\left( -6 \right)=\left| -6+2 \right|+3\]
We can simplify the above step, we get
\[\Rightarrow h\left( -6 \right)=\left| -4 \right|+3\]
Here we can see that, a negative sign is inside the modules, which can be written in positive, where a modulus of a number is always positive,
\[\Rightarrow h\left( -6 \right)=4+3=7\]
Therefore, modulus of a number will be positive.