Question

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

• A. 0
• B. 15.9375
• C. 3
• D. 14.0625

Answer 1

The Correct Option is B

The correct answer is (B): $15.9375$

Given $f(x+y) = f(x)f(y)$

$⇒ f(x) = ax$ (where a is constant ) 

Given, $f(5)=4 ⇒ a^5 = 4⇒ a = 2^{\frac{2}{5}}$

$f(10)-f(-10) = a^{10}-a^{-10}=\bigg(2^{\frac{2}{5}}\bigg)^{10}-\bigg(2^{\frac{2}{5}}\bigg)^{-10}$

= $2^4-2^{-4} = 16-\frac{1}{16} = 15.9375$

Answer 2

Given, $f(5) = 4$
The given function is similar to $f(x) = a^x$
$⇒ a^5 = 4 ⇒ a = 4^{\frac{1}{5}}$
$⇒ f(x) = 4^{\frac{x}{5}}$
$f(10)-f(-10)=16-\frac{1}{16} = 15.9375$