10 The function f is defined by
$$\mathrm { f } ( x ) = 4 + 3 ^ { - x } , x \in \mathbb { R }$$
10
- Using set notation, state the range of f
[0pt]
[2 marks]
10 - The inverse of f is \(\mathrm { f } ^ { - 1 }\)
10
- Using set notation, state the domain of \(f ^ { - 1 }\)
[0pt]
[1 mark]
10
- (ii) Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\)
[0pt]
[3 marks]
10 - The function \(g\) is defined by
$$g ( x ) = 5 - \sqrt { x } , ( x \in \mathbb { R } : x > 0 )$$
10
- Find an expression for gf (x)
[0pt]
[1 mark]
10
- (ii) Solve the equation \(\mathrm { gf } ( x ) = 2\), giving your answer in an exact form.
[0pt]
[3 marks]