What is a Function?
A function can be expressed in many ways, some of them being linear, quadratic, logarithmic functions etc. But just like numbers there are operations which can be used even on functions.
Addition and Subtraction between functions:
If f(x) = 2x+3 and g(x) = 3x+5, then find (f+g)(x) and (f –g)(x).
So, by using the above formula,
(f+g)(x) = 2x+3+3x+5 Combine like terms!
è(f+g)(x) = 5x+8
(f –g)(x) = 2x+ 3 – (3x+5) è 2x+3 – 3x-5
è(f-g)(x) = -x-2
Multiplication and Division of functions:
If f(x) = (x2+ 4), g(x) = (2x+8), find (f.g)(1), (f/g)(1).
So, (f.g)(1) = f(1).g(1)
f(1)=(12+ 4)= 5 and g(1)= 2(1)+ 8= 10
è(f.g)(1)= 5.10 = 50
è(f/g)(1)= f(1) / g(1) = 10/50= 1/2
Composition between functions:
Example: f(x)= 2x+3, g(x)= 3x+5, find fog(x)
f(3x+5)= 2(3x+5) +3
-> 6x+10+3 -> 6x+13 = fog(x)
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