Let N be the set of natural numbers. Define a real valued function f:N→N by f(x)=2x+1. Using this definition, complete the table given below. $\begin{center}
\begin{tabular}{|r|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & 5 & 6 & 7
\hline
y & f(1)=\ldots & f(2)=\ldots & f(3)=\ldots & f(4)=\ldots & f(5)=\ldots & f(6)=\ldots & f(7)=\ldots
\hline
\end{tabular}
\end{center}
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Step-by-Step Solution
Step 1: Understand the Function Definition
The problem defines a function
f(x)=2x+1
. This means that for any input value
x
, we multiply
x
by 2 and then add 1 to get the output value f(x). The domain and codomain are the set of natural numbers
N
.
Step 2: Calculate f(1)
To find
f(1)
, we substitute
x=1
into the function definition. This gives us
2×1+1
.
Step 3: Calculate f(2)
Next, we find
f(2)
by substituting
x=2
into the function. This results in
2×2+1
.
Step 4: Calculate f(3)
For
f(3)
, we substitute
x=3
into the function, yielding
2×3+1
.
Step 5: Calculate f(4), f(5), f(6), f(7)
We continue the process for the remaining values of
x
. For
x=4
,
f(4)=2(4)+1=9
. For
x=5
,
f(5)=2(5)+1=11
. For
x=6
,
f(6)=2(6)+1=13
. For
x=7
,
f(7)=2(7)+1=15
.
Step 6: Complete the Table
By calculating the function values for each given
x
, we can now complete the table.