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If $f(x+y) = f(x) f(y)$ and $f(5) = 4,$ then $f(10) – f(-10)$ is equal to

1. $0$
2. $15.9375$
3. $3$
4. $14.0625$

Given that,

$f(x+y) = f(x) f(y),$ and $f(5) = 4$

Now, $f(10) = f(5+5)$

$\Rightarrow f(10) = f(5) f(5)$

$\Rightarrow f(10) = 4 \times 4$

$\Rightarrow \boxed{ f(10) = 16}$

And, $f(15) = f(5+10)$

$\Rightarrow f(15) = f(5) f(10)$

$\Rightarrow f(15) = 4 \times 16$

$\Rightarrow \boxed{ f(15) = 64}$

We can write $f(5) = f[15+(-10)]$

$\Rightarrow f(5) = f(15) f(-10)$

$\Rightarrow 4 = 64 f(-10)$

$\Rightarrow f(-10) = \frac{4}{64}$

$\Rightarrow \boxed{ f(-10) = \frac{1}{16}}$

Then, $f(10) – f(-10) = 16 – \frac{1}{16} = \frac{256-1}{16} = \frac{255}{16} = 15. 9375$

$\therefore$ The value of $f(10) – f(-10) = 15 . 9375.$

Correct Answer$: \text{B}$
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