SOLUTION: The range of a function f(x) = 4x-5 is (-1, 7) find its domain

Question 846913: The range of a function f(x) = 4x-5 is (-1, 7) find its domain

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the functionm is:
f(x) = 4x- 5
the range is (-1,7)
this means that -1 < x < 7

replace f(x) with those values to see what the corresponding value of x is.

-1 = 4x - 5 is your first equation.
add 5 to both sides to get 4 = 4x
divide both sides by 4 to get x = 1.
when x = 1, 4x - 5= -1
x can't be equal to 1, because then f(x) would be equal to 1 and that's not in the range, so x has to be greater than 1.

7 = 4x - 5 is your second equation.
add 5 to both sides to get 12 = 4x
divide both sides by 4 to get x = 3.
when x = 3, 4x - 5 = 7
x can't be equal to 3, because then f(x) would be equal to 7 and that's not in the range, so x has to be smaller than 1.

your domain is 1 < x < 3

this will lead to a range -1 < f(x) < 7

your graph will look something like this:

the vertical lines are at x = 1 and 3 to show where the value of x has to be between, but not at.

the horizontal lines are at y = -1 and 7 to show where the value of y has to be between, but not at.

you can see from the intersection of the vertical and horizontal lines, that the line of the equation meets at those points.
this confirms that the limits of the domain create the limits of the range.

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