Question

Find the domain and range for the following functions:

a. f: ℝ → ℝ given by f(x) = x + 2
b. g: ℝ → ℝ given by g(x) = √x − 1
c. f(g(x))
d. g(f(x))

Answer 1

Answer with Step-by-step explanation:

Since we have given that

a. f: ℝ → ℝ given by f(x) = x + 2

Domain would be all real numbers i.e. (-∞, ∞)

Range would be all real numbers i.e. (-∞, ∞)

b. g: ℝ → ℝ given by g(x) = √x − 1

Domain would be all positive numbers i.e. [0,∞)

Range would be [-1,∞)

c. f(g(x))

`f(g(x))=f(√(x)+1)=√(x)+1+2=√(x)+3`

Domain would be [0,∞)

Range would be [3,∞)

d. g(f(x))

`g(x+2)=√(x+2)-1`

Domain would be [-2,∞)

Range would be (0,∞)