Euclid 2020/Problem 6

(a) Suppose that the function $g$ satisfies $g(x) = 2x - 4$ for all real numbers $x$ and that $g^-1$ is the inverse function of $g$ . Suppose that the function $f$ satisfies $g(f(g^-1(x))) = 2x^2 + 16x + 26$ for all real numbers $x$ . What is the value of $f(\pi)$ ? (b) Determine all pairs of angles $(x; y)$ with $0 \le x < 180$ and $0 \le y < 180 that satisfy the following system of equations:$ (Error compiling LaTeX. Unknown error_msg)log_2(sin x*cos y) $= -3/2$ $log_2(sin x/cosy)$ = 1/2$

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Euclid 2020/Problem 6