Topic 2.2: Functions: Domain and Range Questions

f(x) = 3x − 5. (a) Find f(4). (b) Find the value of x for which f(x) = 10.

The function g is defined for −2 ≤ x ≤ 5. The graph of g passes through a minimum at (1, −4) and a maximum at (5, 7). Write down (a) the domain of g, (b) the range of g.

The mapping below shows a relationship between set A = {1, 2, 3} and set B = {4, 6, 8}. Each element of A maps to exactly one element of B. (i) State whether this relationship is a function. (ii) Write down the output when the input is 2.

f(x) = 2x + 3 and g(x) = x². (a) Find f(g(x)). (b) Find g(f(2)).

h(x) = x − 4 and k(x) = 3x. Find (a) k(h(x)) and (b) the value of x such that k(h(x)) = 18.

f(x) = 4x − 7. (a) Find f⁻¹(x). (b) Find f⁻¹(5).

g(x) = (x + 2)/3. (a) Find g⁻¹(x). (b) Verify your answer by showing g(g⁻¹(x)) = x.

A function is defined as f(x) = √(x − 3) for x ≥ 3. (a) Write down the domain of f. (b) Find the range of f.

f(x) = 2x + 1 for 0 ≤ x ≤ 4. (a) Find the range of f. (b) A student claims the range is all real numbers. Explain why they are wrong.