Page 195 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes Evidently, f o g # g o f
Similarly, (f o f) (x) = f(f(x) ) = f(3x + 1) [Read as function of function f ].
= 3(3x + 1) + 1
= 9x +3 + 1 = 9x + 4

(g o g)(x) = g(g(x)) = g(x + 2) [Read as function of function g]
2
2
= (x + 2) + 2
2
= x + 4x + 4 + 2
2
4
2
4
= x + 4x + 6
6.6 Summary
The sum of two odd functions is odd, and any constant multiple of an odd function is odd.
The product of two even functions is an even function.
The product of two odd functions is an even function.
The integral of an odd function from A to +A is zero (where A is finite, and the function has
no vertical asymptotes between A and A).
The integral of an even function from A to +A is twice the integral from 0 to +A (where A
is finite, and the function has no vertical asymptotes between A and A).
A rational function is defined as the quotient of two polynomial functions.
f(x) = P(x) / Q(x)

6.7 Keywords

Functions: Functions are mathematical ideas that take one or more variables and produce a
variable.
Logarithmic Function: It is defined as inverse of exponential functions.
Odd Function: The graph of an odd function has rotational symmetry with respect to origin.

Rational Funciton: It is defined as the quotient of two polynomial functions.

6.8 Self Assessment

1. The graph of even function is ………… with respect to y-axis, meaning that its graph
remain unchanged after reflection about y-axis.

2. The roots of a function are defined as the point where the function …………
3. The Investigation of ………… function is carried by changing parameter included in the
formula of the function.

4. The graph of an ………… function has rotational symmetry with respect to the origin.
t
5. ………… is denoted mathematicaly by e and in matlab by exp(t).
6. An invertible function is a function that can be …………

7. If f(x) be a real valued function of a real variable then f is even function is equals to …………

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