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The function $f(x)$ satisfies \[f(x) - 2 f \left( \frac{1}{x} \right) = 4^x\]for all $x \neq 0.$ Find $f(2).$

 Sep 30, 2020
 #2
avatar+111144 
+1

Hint 

 

\(f(2)-2f(\frac{1}{2})=4^2\\ and\\ f(\frac{1}{2})-2f(2)=4^{0.5}\)

 

 

solve these simultaneously to find f(2)

 

 

 

Please let asker guest finish this.

 Sep 30, 2020
 #3
avatar
+1

Thanks! Is the answer $-\frac{20}{3}$? Because that is what I got...

Guest Sep 30, 2020
 #4
avatar+111144 
+1

Yes, I got that as well.

Melody  Sep 30, 2020

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