# Operations on Functions Calculator

## Perform operations on functions step by step

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

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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

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