Question

Let f(x) = (x - 1)/(-x2 + 2)
How to find the domain (Steps please)

Than solve for f(x)= 1/2

Answer 1

F(x) = (x-1)/(-x^2+2).

Any value of x that causes the denominator to become zero is not in the domain. Because a zero denominator
means an undefined fraction.

Denominator = -x^2 + 2 = 2- x^2.
Set the denominator equal to zero and
solve for x:

2 - x^2 = 0,
-x^2 = -2,
x^2 = 2,
x = +-sqrt(2) results in a denominator
of zero, and is,therefore, NOT in the
domain.

So the domain is all real values of x
except +- sqrt(2).

F(1/2) = (1/2-1) / (2-(1/2)^2,
F(1/2) = (-1/2) / (2-1/4),
F(1/2) = (-1/2) / (7/4),
F(1/2) = (-1/2) * 4/7 = -4/14 = -2/7.