Question

Find the relationship between between the functions$g\left(x\right)+10\mathrm{and}f\left(x\right)$.

Short answer

The relationship between between the functions$f\left(x\right)andg\left(x\right)aref\left(x\right)=g\left(x\right)+10.$

Step-by-step solution

Step 1. Given

The given two functions are$f\left(x\right)andg\left(x\right)$.

Step 2.  Explanation

$$\begin{gathered} \mathrm{The}\mathrm{function}\mathrm{g}\left(\mathrm{x}\right)\mathrm{be}\mathrm{the}\mathrm{antiderivatives}\mathrm{of}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right). \\ \mathrm{then}\mathrm{g}\text{'}\left(\mathrm{x}\right)=\mathrm{f}\left(\mathrm{x}\right)\mathrm{Rewrite}\mathrm{the}\mathrm{antiderivative}\mathrm{of}\mathrm{function}\mathrm{as}, \\ \mathrm{If}\mathrm{g}\left(\mathrm{x}\right)\mathrm{be}\mathrm{the}\mathrm{antiderivatives}\mathrm{of}\mathrm{function}\mathrm{f}\left(\mathrm{x}\right)\mathrm{then},\mathrm{write}\mathrm{the}\mathrm{form}\mathrm{as}\mathrm{g}\left(\mathrm{x}\right)+\mathrm{C},\mathrm{where}\mathrm{Cis}\mathrm{a}\mathrm{constant}. \\ LetC=10. \\ Then,g\left(x\right)+C=f\left(x\right)(Sinceg\text{'}(x)=f(x\left)\right)g\left(x\right)+10=f\left(x\right) \\ \mathrm{Therefore},\mathrm{the}\mathrm{relationship}\mathrm{between}f\left(x\right)andg\left(x\right)aref\left(x\right)=g\left(x\right)+10 \end{gathered}$$