Simulation · Maths · Class 11

Adding and dividing functions point by point

From the lesson Algebra of real functions in Relations and Functions. Change the values and watch what happens.

Adding and dividing functions point by pointMaths · Class 11

The idea behind it

NCERT §2.4.2

Let f and g be real functions with the same domain X ⊂ R. Their sum and difference work value by value: (f + g)(x) = f(x) + g(x) and (f − g)(x) = f(x) − g(x) at every x in X.
For a real number α (a scalar), the function αf is defined by (αf)(x) = α·f(x), x ∈ X.
The product is (fg)(x) = f(x)·g(x), x ∈ X; this is called pointwise multiplication.
The quotient is (f/g)(x) = f(x)/g(x), defined only where g(x) ≠ 0. Its domain is X with the zeros of g removed.
Example: with f(x) = 3x − 2 and g(x) = x + 1 on R, (f + g)(x) = 4x − 1, (f − g)(x) = 2x − 3, (fg)(x) = 3x² + x − 2, (2f)(x) = 6x − 4, and (f/g)(x) = (3x − 2)/(x + 1) for x ≠ −1.
When f and g have different natural domains, the combined function lives on the common part. For f(x) = √x and g(x) = x − 4, f + g is defined on [0, ∞), and f/g on [0, ∞) − {4}.