a The center b The radius c xintercepts 2 For the functions

a) The center b) The radius c) x-intercepts 2. For the functions f(x)- g(x)-x-1 compute the algebraic combinations below. Simplify your expressions and state t restriction(s) of the resulting function. Domain restriction: Domain restriction: Domain restriction: Ug)() Page 1

Solution

f(x) = 2 / (x^2 -1 )

g(x) = x / (x-1)

(f+g)(x) = f(x) + g(x)

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

= {2 + x ( x+1) } / ( x^2 -1 )

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

restriction on domain is all values of x except + 1 and -1

2) (f-g)(x) = f(x) - g(x)

2 / (x^2 -1 ) - x/ (x-1)

( 2 - x^2 - x ) / ( x^2 -1 )

restriction on domain is all values of x except + 1 and -1

3) (f/g)(x) = f(x) / g(x)

=  2 / (x^2 -1 ) / x / (x-1)

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

= 2 / x ( x+1)

restriction on domain is all values of x except 0 and -1