TMUA Y and A Tutoring Paper 1 with Answers and Hints · Question 16

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Y and A Tutoring Paper 1 with Answers and Hints · Q16

Paper 1Functions & graphs

A function $f$ is defined for all real numbers and has the property that $f(x+y)=f(x)f(y)$ for all real numbers $x$ and $y$ .

It is given that there exists at least one real number $a$ such that $f(a)\ne0$ .

If $f(4)=16$ which of the following is the only possible value for $f(-2)$ ?

-4

-\frac14

\frac1{16}

\frac14

4

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