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Euclid 2020/Problem 6

Revision as of 03:28, 31 March 2023 by Tonyliu (talk | contribs) (Created page with "(a) Suppose that the function <math>g</math> satisfies <math>g(x) = 2x - 4</math> for all real numbers <math>x</math> and that <math>g^-1</math> is the inverse function of <ma...")
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(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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