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Given that (2,3) is on the graph of y=f(x), find a point on the graph of y=f(2x+1)+3. Express your answer as an ordered pair (a,b) where a and b are real numbers.

 Feb 12, 2019
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Given that (2,3) is on the graph of y=f(x), find a point on the graph of y=f(2x+1)+3. 

Express your answer as an ordered pair (a,b) where a and b are real numbers.

 

\(\begin{array}{|rcll|} \hline y &=& f(x) \quad | \quad (x=2,\ y= 3 )\\ 3 &=& f(2) \\ \mathbf{f(2)} & \mathbf{=} & \mathbf{3} \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline y &=& f(2x+1)+3 \\\\ 2x+1 &=& 2 \\ 2x &=& 1 \\ \mathbf{x} & \mathbf{=} & \mathbf{\dfrac{1}{2}} \\\\ y &=& f(2) + 3 \quad | \quad \mathbf{f(2)=3} \\ y &=& 3 + 3 \\ \mathbf{y} & \mathbf{=} & \mathbf{6} \\ \hline \end{array}\)

 

\((a,b) = \left( \dfrac{1}{2},\ 6 \right) \)

 

laugh

 Feb 13, 2019

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