2023HSCShort answer

Q14 (a) (ii)

2 marks

Question

Let $f(x)=2x+\ln x$ , for $x>0$ .

(ii) Let $g(x)=f^{-1}(x)$ . By considering the value of $f(1)$ , or otherwise, evaluate $g'(2)$ .

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct solution	2
Finds $g'(x)$ or $f'(1)$ , or equivalent merit	1

Sample answer:

f(1)=2\text{ therefore }g(2)=1

g'(x)=\frac{1}{f'(g(x))}

g'(2)=\frac{1}{f'(g(2))}=\frac{1}{f'(1)}=\frac13

Supplied marking guidance · human reviewed

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Syllabus alignment

Functions

Further Work with FunctionsUse algebraic and graphical representations of functions and inverse functions to model and solve problems.

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