Question

find the inverse function and give the table values of each of the following functions (show your solutions and use the value from -2 to 2)​

Answer 1

Answer:

here is your answer

Step-by-step explanation:

We use the symbol f - 1 to denote an

inverse function. For example, if F(x) and g(x) are inverses of each other, then we can symbolically represent this statement as:

g(x) = f - 1(x) or f(x) = g - 1(x)

One thing to note about the inverse

function is that the inverse of a function is not the same as its reciprocal, i.e., f - 1 fx) ne1/f(x) This article will discuss how to find the inverse of a function.

Since not all functions have an inverse, it

is therefore important to check whether a

function has an inverse before embarking

on determining its inverse.

We check whether or not a function has an inverse in order to avoid wasting time trying to find something that does not exist.

One-to-one functions

So how do we prove that a given function has an inverse? Functions that have inverse are called one-to-one functions. A function is said to be one-to-one if, for

each number y in the range of f, there is

exactly one number x in the domain of f

such that f(x) = y

In other words, the domain and range of

one-to-one function have the following

relations:

Domain of f - 1 = Range of f. one to one function given, f(a) = 3a + 5 and f(b) = 3b + 5

Range of f - 1 = Domain off. For example, to check if f(x) = 3x + 5 is

Rightarrow3a+5=3b+5

Rightarrow3a=3b

Rightarrow a=b.

Therefore, f(x) is one-to-one function because, a = b

Consider another case where a function f is given by f=\ (7,3),(8,-5),(-2,11),(-6 4)\ This function is one-to-one because none of its y - values appear more than once.

What about this other function h=\ (-3 , 8),(-11,-9),(5,4),(6,-9)\ ? Function h is not one-to-one because the y- value of -9 appears more than once.

You can also graphically check one-to-one function by drawing a vertical line and horizontal line through a function graph. A function is one-to-one if both the horizontal and vertical line passes through the graph once.