Functions!! please help show all work please!

Question

Use f(x)= 3-x over x^2 -x and g(x)= ROOT 6-2x

a) f(-3)= ? b) f(g(1))= ?

c) For what x, if any, is f(x)=0?

what is the domain and range of g?

Domain: _______? Range:______?

Answer 1

a)

f(x) = (3-x)/x^2

f(-3) = (3 -(-3))/(-3)^2 = 6/9 = 2/3

b)

g(1) = Sqrt(6-2(1)) = Sqrt(6-2) = Sqrt(4) = 2

f(g(1)) = f(2) = (3 -(2))/(2)^2 = 1/4

c)

(3-x)/x^2 = 0

(3-x) = 0

-x = -3

x = 3

Domain: [-infinity,3], since you can't take the square root of a negative number

Range: [0,sqrt(infinity)], since the lowest number it can be is zero, and the highest number is infinity