Find domain, codomain and range of the following function. (¡) A={-2,3,4}
F:A—>R such that F(x)=x³-2
(¡¡) A={-1,0,1,3,4}
g:A—>Z such that g(x)=2x-1
(¡¡¡) A:{X:x is a pri number <8}
h:A—>N such that h(x)=(x²+1)-x
Answers
Answer:
The domain of a function is the set of input values, xx, for which a function is defined. The domain is shown in the left oval in the picture below. The function provides an output value, f(x)f(x), for each member of the domain. The set of values the function outputs is termed the range of the function, and those values are shown in the right hand oval in the picture below. A function is the relation that takes the inputs of the domain and output the values in the range. The rule for a function is that for each input there is exactly one output.

Mapping of a Function:The oval on the left is the domain of the function ff, and the oval on the right is the range. The green arrows show how each member of the domain is mapped to a particular value of the range.
As you can see in the illustration, each value of the domain has a green arrow to exactly one value of the range. Therefore this mapping is a function.
We can also tell by the set of ordered pairs given in this mapping that it is a function because none of the xx-values repeat: (−1,1),(1,1),(7,49),(0.5,0.25)(−1,1),(1,1),(7,49),(0.5,0.25); since each input maps to exactly one output. (Note that although the output value of 11 repeats, only the input values can not repeat)
We can also tell this mapping, and set of ordered pairs is a function based on the graph of the ordered pairs because the points do not make a vertical line. If an xxvalue were to repeat there would be two points making a graph of a vertical line, which would not be a function. Let’s look at this mapping and list of ordered pairs graphed on a Cartesian Plane.
step-by- step explenatoin : pairs: This mapping or set of ordered pairs is a function because the points do not make a vertical line. This is called the vertical line test of a function. It shows that for every input there is exactly one output value.