Let fx squareroot x 2 and gx x 5 Find fg1 Show work Find

Let f(x) = squareroot x + 2 and g(x) = x - 5. Find (f/g)(-1). Show work. Find the domain of the quotient function f/g. Explain.

Solution

given f(x) = sqrt(x+2), g(x)=x-5

a) (f/g)(x) = f(x)/g(x) = sqrt(x+2)/(x-5)

(f/g)(-1) = sqrt(-1+2)/(-1-5) = -1/6

b) domain of f/g is

inside the square must be greater than zero ie x+2 >= 0

x >= -2

denominator is always is not equal to zero x-5 = 0

x = 5

the domaine of f/g is - 2 <= x < 5 or x > 5