Activity Questions 1.9

Q1. Suppose f : ℤ → ℤ is a function defined by f(k) = k³ + 4k - 10. The value of f(k) at k = 4 is ______

This is a fill-in-the-blank question asking for a numerical answer.

Q2. Let f(x) = |x| + 5 and Dom(f) = {c ∈ ℝ | f(x) ∈ ℝ}. Which of the following is(are) true?

□ Domain of f(x) is ℝ

□ Range of f(x) is ℝ

□ Domain of f(x) is [5, ∞)

□ Range of f(x) is [5, ∞)

Q3. Let f : ℝ → ℝ be a function and f(x) = |(x + 4)(4x - 10)|. Which of the following is(are) true?

○ f is an injective function

○ f is a surjective function

○ f is a bijective function

○ None of these

Q4. Which of the following statement(s) is(are) false?

□ Range of a function is a subset of co-domain

□ A function is bijective if and only if it is both injective and surjective

□ Every relation is a function

□ Co-domain of a function is a subset of domain

Q5. Let x ⊂ ℝ and DOM(f) = {x ∈ ℝ | f(x) ∈ ℝ}. Which of the following functions is(are) injective?

□ f(x) = √(10 - x)

□ f(x) = (7x + 6)/(3x)

□ f(x) = 2x + 9

□ f(x) = ((5x + 4)(2x - 3))/2

Q6. Suppose f : ℤ → ℤ is a function defined by f(x) = ax + b. For which of the following integer values of a and b, is the given function bijective?

○ a = 0, b ∈ {z | z ∈ ℤ}

○ a ∈ {-1, 1}, b ∈ {z | z ∈ ℤ}

○ b ∈ {-1, 1}, a = 0

○ b = 0, a ∈ {z | z ∈ ℤ}