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.

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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

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

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

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

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