Chapter 6.4, Problem 4MCQ

To determine

The value of $\left(\frac{f}{g}\right)\left(x\right)$ for the pair of functions $f\left(x\right)=2x^2+4x-3\text{ and }g\left(x\right)=5x-2$ .

Answer to Problem 4MCQ

The value $\left(\frac{f}{g}\right)\left(x\right)$ is equal to $\frac{2x^2+4x-3}{5x-2};x\ne \frac{2}{5}$ for the pair of functions $f\left(x\right)=2x^2+4x-3\text{ and }g\left(x\right)=5x-2$ .

Explanation of Solution

Given information: The given functions are,

  $\left(\begin{array}{l}f\left(x\right)=2x^2+4x-3\\ g\left(x\right)=5x-2\end{array}\right)\mathrm{......}\left(1\right)$

Calculation: Evaluating $\left(\frac{f}{g}\right)\left(x\right)$ using (1),

  $\begin{array}{c}\left(\frac{f}{g}\right)\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}\mathrm{.....}\left(\text{where }g\left(x\right)\ne 0\right)\\ =\frac{2x^2+4x-3}{5x-2}\mathrm{......}\left(\text{where }5x-2\ne 0\right)\\ =\frac{2x^2+4x-3}{5x-2};x\ne \frac{2}{5}\end{array}$