Question

The functions f and g are defined as follows.

f(x)= 1/(x+2)

g(x)= square root of: (x-1)

(a)
State which value of x cannot be included in the domain of f.

(b)
Find the inverse of g(x)


(c) Calculate fg(10)

Answer 1

Answer:

x != -2, x^2 + 1, 1/5

Step-by-step explanation:

(a) It can be understood that nothing can divide 0

thus denominator cannot be 0 meaning x cannot be -2.

(-2 + 2) = 0

(b) y = sqrt(x-1)

inverse meaning we make x the subject

square both sides

y^2 = x - 1

y^2 + 1 = x

inverse = x^2 + 1

(c) composite function:

pass g(10) as domain of f

g(10) = 3, f(3) = 1/(5) = 1/5