Section II Part B — Full Practice Exam 2

<p>(A) The functions $$f$$ and $$g$$ are given by</p><p>$$f(x)=\log_9(x^2+2x+5)-\log_9(x+4)$$</p><p>$$g(x)=7e^{3-2x}-5$$</p><p>(i) Rewrite $$f(x)$$ as a single logarithm base $$9$$ without negative exponents.</p><p>(ii) Using your answer from (i), solve $$f(x)=\frac{1}{2}$$ for all values of $$x$$ in the domain of $$f$$.</p><p>(iii) Solve $$g(x)=9$$ for all values of $$x$$ in the domain of $$g$$.</p><p><br></p><p>(B) The function $$k$$ is given by</p><p>$$k(x)=\cos(2x)+\sin(x)$$</p><p>(i) Rewrite $$k(x)$$ in terms of $$\sin(x)$$ only.</p><p>(ii) Using your answer from (i), solve $$k(x)=0$$ for all values of $$x$$ in the interval $$[-\pi,\pi]$$.</p><p><br></p><p>(C) The function $$h$$ is given by</p><p>$$h(x)=\tan\left(\cos^{-1}\left(\frac{2}{x}\right)\right)$$</p><p>Find all values in the domain of $$h$$ that yield an output value of $$\frac{\sqrt{5}}{2}$$.</p>