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 \(f(x) = a^x\)
\(⇒ a^5 = 4 ⇒ a = 4^{\frac{1}{5}}\)
\(⇒ f(x) = 4^{\frac{x}{5}}\)
\(f(10)-f(-10)=16-\frac{1}{16} = 15.9375\)