Question

Let f of x equals x squared minus 1 and g of x equals x plus 1.



What is the range of StartFraction f of x over g of x EndFraction?

Answer options with 5 options
A.
all real numbers

B.
all real numbers except 0

C.
all real numbers except negative 1

D.
all real numbers except negative 1 and 1

E.
all real numbers except negative 2

Answer 1

f(x)/g(x) = (x^2 - 1)/(x+1) = (x-1)(x+1)/(x+1) = x - 1 for x ≠ -1.
Since x = -1 is not allowed, the value -2 (which would occur at x = -1) is excluded. Thus the range is all real numbers except -2.

Answer: E.