Q. 16 - Calculus

Question

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

Step-by-Step Solution

Answer

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

Step 1. Given

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

Step 2. Explanation

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