what is inverse? can i have some examples?

Answer 1

depends what you are talking about. the general definition of an inverse is,

A*(A)^(-1)=1, where (A)^(-1) is the inverse of A. For a multilicative inverse this is true, but for an additive inverse, we have a+(-a)=0, where (-a) is the additive inverse of a.

for a number, say 83, its inverse is (83)^(-1)=1/83. e.g. (x)^(-1)=1/x for any real number (excluding zero). Zero does not have a multiplicative inverse. For Matrices we have B*B^(-1)=I, where I is the identity matrix

Answer 2

An Inverse is the reverse mapping example X to Y {x^2=y}

The inverse is Y to X {y^(1/2)=x}, if the mapping is combined you get the trivial mapping X to X {x=x} Or Y to Y {y=y} IE {[x^2}^(1/2)=x}

graphically an inverse is a reflection in the line x=y.

This is a simplification

Answer 3

The inverse of a number is that which, when applied under an operation, returns the identity under that operation.

For example, the identity under multiplication is 1, in that N x 1 = N, where N is any number. Under addition, the identity is 0 (N+0=N).
The inverse of N is such that N(operation)inverse = identity.

For multiplication this would be N x 1/N = 1, and for addition it is N+(-N)=0.

Answer 4

Example 1: Find the inverse function of f given by



f(x) = 2x + 3
Solution to example 1:
write the function as an equation.
y = 2x + 3


solve for x.
x = (y - 3)/2


now write f-1(y) as follows .
f -1(y) = (y - 3)/2
or
or f -1(x) = (x - 3)/2


Check
f(f -1(x))=2(f -1(x)) + 3


=2((x-3)/2)+3

=(x-3)+3

=x


f -1(f(x))=f -1(2x+3)


=((2x+3)-3)/2

=2x/2

=x

conclusion: The inverse of function f given above is f -1(x) = (x - 3)/2

Matched Exercise 1: Find the inverse function of f given by



f(x) = -x - 4

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Example 2: Find the inverse function of f given by

f(x) = (x - 3)2, if x >= 3
Solution to example 2:

write the function as an equation.

y = (x - 3)2



solve for x, two solutions .

x = 3 + sqrt(y)


x = 3 - sqrt(y)


the first solution is selected since x >= 3, write f-1(y) as follows.


f -1(y) = 3 + sqrt(y)


or


f -1(x) = 3 + sqrt(x)


Check

f(f -1(x))=((3+sqrt(x))-3)2


=(sqrt(x))2


=x


f -1(f(x))=3+sqrt((x-3)2)


=3+|x-3| (since x >= 3, x-3 >= 0, |x-3| = x-3)


=3+(x-3)


=x

conclusion:
The inverse of function f given above is f -1(x) = 3 + sqrt(x)

Answer 5

if F is function such that F(x) = y (maps x onto y), the inverse function G (or F^-1) maps y onto x (G(y) = x) in such a way that it is one to one.

Answer 6

The inverse operation is doing something opposite of doing something (wtf o.o). Like the inverse operation of + is - and divide is multiply and vice-versa.