Question:

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

Updated On: Aug 20, 2024
  • 0
  • 15.9375
  • 3
  • 14.0625
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The Correct Option is B

Approach Solution - 1

The correct answer is (B): 15.937515.9375

Given f(x+y)=f(x)f(y)f(x+y) = f(x)f(y)

f(x)=ax⇒ f(x) = ax (where a is constant ) 

Given, f(5)=4a5=4a=225f(5)=4 ⇒ a^5 = 4⇒ a = 2^{\frac{2}{5}}

f(10)f(10)=a10a10=(225)10(225)10f(10)-f(-10) = a^{10}-a^{-10}=\bigg(2^{\frac{2}{5}}\bigg)^{10}-\bigg(2^{\frac{2}{5}}\bigg)^{-10}

2424=16116=15.93752^4-2^{-4} = 16-\frac{1}{16} = 15.9375

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Approach Solution -2

Given, f(5)=4f(5) = 4
The given function is similar to f(x)=axf(x) = a^x
a5=4a=415⇒ a^5 = 4 ⇒ a = 4^{\frac{1}{5}}
f(x)=4x5⇒ f(x) = 4^{\frac{x}{5}}
f(10)f(10)=16116=15.9375f(10)-f(-10)=16-\frac{1}{16} = 15.9375
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