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Operations on Functions Calculator

Perform operations on functions step by step

The calculator will add, subract, multiply, and divide two functions f(x)f(x) and g(x)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(x)=2x−1f{\left(x \right)} = 2 x - 1 and g(x)=3x+5g{\left(x \right)} = 3 x + 5.

Solution

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

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

(f⋅g)(x)=(2x−1)⋅(3x+5)=(2x−1)(3x+5)\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)

(fg)(x)=(2x−1)(3x+5)=2x−13x+5\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

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

(f−g)(x)=−x−6\left(f - g\right)\left(x\right) = - x - 6A

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

(fg)(x)=2x−13x+5\left(\frac{f}{g}\right)\left(x\right) = \frac{2 x - 1}{3 x + 5}A