Answer:
{-3, 2, 7, ...... } is the range of given function.
Step-by-step explanation:
We are given that the function is defined as:
[tex]y = 5x + 2[/tex] where [tex]x > -2[/tex].
To find:
Range of the given function = ?
Solution:
First of all, let us have a look at the definition of Domain and Range.
Domain of a function f(x) is the set of input that is valid i.e. the value of x which are valid.
For example, in the given question, x > -2 i.e. x can be any value from the set {-1, 0, 1, 2, ......} is the domain of given function.
Range of a function f(x) is the set of output that is valid according to the input given.
For the given equation, let us put the value of x one by one and try to find out the value of y.
Putting x = -1 first:
[tex]y = 5 \times -1+2\\\Rightarrow y=-3[/tex]
Putting x = 0:
[tex]y = 5 \times 0+2\\\Rightarrow y=2[/tex]
Putting x = 1:
[tex]y = 5 \times 1+2\\\Rightarrow y=7[/tex]
So, the range is : {-3, 2, 7,......}
