Please help me!? domain and range question of a polynomial..?

Question

(5x-3) / (2x +1)

what is the domain and range?? and how did you figure that out?

thankssssssss <3

Answer 1

f(x) = (5x - 3) / (2x + 1)

The domain is all possible x values that can be entered into the function.  Since you can&#039;t divide by zero, whatever x values makes the denominator of the fraction zero will not be in the domain.  Set the denominator equal to zero and solve for x to find this value.

2x + 1 = 0

2x = -1

x = -½

Then the domain is (-∞, -½) U (-½, ∞)

The range is all y or f(x) values that the function can return.  Remember that the range of f(x) is the same as the domain of f^(-1)(x), the inverse function of f(x).  To find the inverse function, switch x and y and solve for y.

x = (5y - 3) / (2y + 1)

(2y + 1)x = 5y - 3

2xy + x = 5y - 3

2xy - 5y = -x - 3

y(2x - 5) = -x - 3

y = -(x + 3) / (2x - 5)

f^(-1)(x) = (x + 3) / (5 - 2x)

You now want the domain of f^(-1)(x) which is the same process as before.  Find the x value which makes the denominator of the fraction zero.  This value can&#039;t be in the domain.

5 - 2x = 0

5 = 2x

5/2 = x

Then the range of f(x) is (-∞, 5/2) U (5/2, ∞)

Hope this helps you!