CAIE IGCSE Additional Math 1.5 Explain When Inverses Do Not Exist Questions

Practise Cambridge IGCSE Additional Mathematics by deciding when inverses exist, solving for inverse rules and stating valid inverse domains.

Exam points

Determine whether an inverse function exists by testing whether the function is one-one.
Find an inverse function algebraically by interchanging variables and solving for the original input.
State the domain of an inverse function using the range of the original function and any restrictions.

[Maximum number: 4]

The functions f and g are defined as follows, for all real values of x.

$\begin{aligned}f(x)&=2x^2-1\\g(x)&=e^x+1\end{aligned}$

For each of the functions f and g , either explain why the inverse function does not exist or find the inverse function, stating its domain.

f is not one-one, hence $f^{-1}$ does not exist oe.
$g^{-1}(x)=\ln(x-1)$
M1 for $x=\ln(y-1)$ and a swap of variables at some point;
or $y=\ln(x+1)$ ;
or $e^x=y-1$ and $y=\ln x-1$ .

Domain: x>1. B1.

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CAIE IGCSE Additional Math 1.5 Explain When Inverses Do Not Exist Questions question 1