Question 74

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

Solution

The given function is equivalent to f(x) = $$a^x$$

Given, f(5) = 4

=> $$a^5=4=>\ a=4^{\frac{1}{5}}$$

=> f(x) = $$4^{\frac{x}{5}}$$

f(10) - f(-10) = 16 - 1/16 = 15.9375

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