Functions

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A function is a rule in which, for every input it produces a single output.

Function Image

Here the function is f(x) = 2x. For every input value x, the output value is doubled.

Domain is the set of x values whereas Range is the set of y values.

Injective function:
It is also called as one-one function. For two different input values a and b there there should be unique output values that is f(a) ≠ f(b).

Surjective function:
It is also called as onto function. For every element in the codomain or range there is an x in the domain.

1) Find the inverse of the function y = x/4 - 6
Answer: y = x/4 - 6
4 y = 4 (x/4 – 6 )
4y = x – 24
x = 4y + 24
f^(-1)(x) = 4x + 24

2) If f(x) = -4x and g(x) = -x + 8, find (f . g) (3)
Answer: (f . g) (3) = f [g(3)]
g(3) = - 3 + 8 = 5
f [g(3)] = f [5]
          = -4 (5) = -20

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