Topic 2.2: Functions: Domain and Range Questions

Write down the value of $f(4)$.

f(x) = 3x − 5.

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.

The function f is defined by f(x) = 3x − 7.

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).

The function f is defined by f(x) = √(x − 3) + 2. Write down the domain and the range of f.

The function h is defined by h(x) = 2x² − 3. Find h(−2), and solve h(x) = 15.

A relation between x and y is given by the table: x = 1, 2, 3, 4 and y = 5, 8, 8, 11 respectively. Explain whether this relation is a function, and state the value of y when x = 3.

Interpret this domain in context.

g(x) = (x + 2)/3.

f(x) = 2x + 1 for 0 ≤ x ≤ 4.

A function is defined as f(x) = √(x − 3) for x ≥ 3.

The function g is defined by g(x) = (x + 4)/2 for all real x.

A phone-repair shop charges a fixed call-out fee plus an hourly rate. The total cost, in dollars, of a repair lasting t hours is modelled by C(t) = 35t + 20, for t ≥ 0.

(a) Find C(2.5).

(b) State what your answer to part (a) represents.

f(x) = 4x − 7.

A function is defined by g(x) = 8/(x − 2) + 5, for 2 < x ≤ 6.

Interpret the meaning of $C^{-1}(500)$.

Write down $f^{-1}(x)$.

Sketch the graph of $y=f^{-1}(x)$ on the same axes.

The temperature of a metal rod, in °C, m minutes after it is removed from a furnace is modelled by H(m) = 480 × 0.92^m + 20, for m ≥ 0.

(a) Write down the temperature of the rod at the instant it is removed from the furnace.

(b) Find H(15), correct to three significant figures.