# Operations on Functions Calculator

The calculator will find the sum, difference, product, and quotient of the functions. It will also evaluate the resulting functions at the specified point, if needed.

## Your Input

**Find the sum, difference, product, and quotient of $$$f = 2 x - 1$$$ and $$$g = 3 x + 5$$$ at the point $$$3$$$.**

## Solution

$$$f + g = \left(2 x - 1\right) + \left(3 x + 5\right) = 5 x + 4$$$

$$$f - g = \left(2 x - 1\right) - \left(3 x + 5\right) = - x - 6$$$

$$$f\cdot g = \left(2 x - 1\right)\cdot \left(3 x + 5\right) = 6 x^{2} + 7 x - 5$$$

$$$\frac{f}{g} = \frac{\left(2 x - 1\right)}{\left(3 x + 5\right)} = \frac{2 x - 1}{3 x + 5}$$$

## Answer

**$$$f + g = 5 x + 4$$$A**

**$$$\left(f + g\right)\left(3\right) = 19$$$**

**$$$f - g = - x - 6$$$A**

**$$$\left(f - g\right)\left(3\right) = -9$$$**

**$$$f\cdot g = 6 x^{2} + 7 x - 5$$$A**

**$$$\left(f\cdot g\right)\left(3\right) = 70$$$**

**$$$\frac{f}{g} = \frac{2 x - 1}{3 x + 5}$$$A**

**$$$\left(\frac{f}{g}\right)\left(3\right) = \frac{5}{14}\approx 0.357142857142857$$$**