# Operations on Functions Calculator

The calculator will add, subract, multiply, and divide two 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

Optional.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

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

## Solution

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

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

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

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

$\left(f + g\right)\left(x\right) = 5 x + 4$A
$\left(f - g\right)\left(x\right) = - x - 6$A
$\left(f\cdot g\right)\left(x\right) = \left(2 x - 1\right) \left(3 x + 5\right)$A
$\left(\frac{f}{g}\right)\left(x\right) = \frac{2 x - 1}{3 x + 5}$A