3.1.4 Algebra and functions (A-level only)

The function $f$ is defined by

\text{ for } x \in \mathbb{R}

The function $g$ is defined by

g(x) = e^{2x} + 15

where $g$ has its greatest possible domain.

a.

Using set notation, state the range of $f$ .

[1]

b.

State the domain of $g$ .

[1]

c.

The composite function $h$ is given by

\text{ for } x \in \text{domain of } g

(i) Write down an expression for $h (x)$ in terms of $x$ . (ii) Determine if $h$ has an inverse. Fully justify your answer.

[3]

3.1.4 Algebra and functions (A-level only)

The function $f$ is defined by

\text{ for } x \in \mathbb{R}

The function $g$ is defined by

g(x) = e^{2x} + 15

where $g$ has its greatest possible domain.

a.

Using set notation, state the range of $f$ .

[1]

b.

State the domain of $g$ .

[1]

c.

The composite function $h$ is given by

\text{ for } x \in \text{domain of } g

(i) Write down an expression for $h (x)$ in terms of $x$ . (ii) Determine if $h$ has an inverse. Fully justify your answer.

[3]

3.1.4 Algebra and functions (A-level only)

3.1.4 Algebra and functions (A-level only) Questions