2023HSCShort answer

Q14 (a) (i)

1 mark

Question

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

(i) Explain why the inverse of $f(x)$ is a function.

Try the question before revealing the answer.

Solution

Criteria	Marks
Provides correct explanation	1

Sample answer:

f'(x)=2+\frac1x>0\quad\text{for }x>0

$f$ is always increasing. Therefore, since $f$ is one-to-one for $x>0$ , $f$ has an inverse function.

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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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