Find the domain and range of the following function.

F(x) = 1/(7-x)(x^2 -1)

Question

Find the domain and range of the following function.

F(x) = 1/(7-x)(x^2 -1)

brooksn · Answer

Mathway and/or photomath will help you with these questions.

jhonyy9 · Answer

- like a first think bc. the denominator of a fraction not can being zero so what will be the restriczions first of ALL ?

hope this will help you begining solve it

Ballery1 · Answer

Thanks for the suggestion mate.

Narad · Answer

$$f(x)=(x ^{2}-1)/(7-x)$$
For the domain, the denominator must be different than zero
$$7-x \neq0$$

For the range, let
$$y=(x ^{2}-1)/(7-x)$$
$$y(7-x)=x ^{2}-1$$
$$7y-yx=x ^{2}-1$$
$$x^{2}+yx-(7y+1)=0$$
For this quadratic equation  in "x"to have solutions, the discriminant is$$\Delta \ge 0$$
$$\Delta = b ^{2}-4ac = y^{2}-4*1*(-(7y+1)) \ge 0$$
$$y ^{2}+28y+4 \ge 0$$
The solutions to this equations are
$$y1=(-28-\sqrt{28^{2}-4*1*4})/2$$
and
$$y2=(-28+\sqrt{28^{2}-4*1*4})/2$$
The range is 
$$y \epsilon (-\infty , y1] \cup [y2, +\infty )$$