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# moar functional equations

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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
+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)

Sep 30, 2020
#3
+1

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

Guest Sep 30, 2020
#4
+111144
+1

Yes, I got that as well.

Melody  Sep 30, 2020