# Operations on Functions Calculator

The calculator will find the sum $(f+g)(x)$, difference $(f-g)(x)$, product $(fg)(x)$, and quotient $\left(\frac{f}{g}\right)(x)$ of the functions $f(x)$ and $g(x)$, with steps shown. It will also evaluate the resulting functions at the specified point if needed.

Related calculator: Composite Function Calculator

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## Your Input

Find the sum, difference, product, and quotient of $f{\left(x \right)} = 2 x - 1$ and $g{\left(x \right)} = 3 x + 5$.

## Solution

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

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

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

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

## Answer

$\left(f + g\right)\left(x\right) = 5 x + 4$

$\left(f - g\right)\left(x\right) = - x - 6$

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

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