a. Find the inverse of the given function. b. Prove that the three properties below hold true using the given function and its inverse. - The inverse of \( f^{-1}(x) \) is \( f(x) \). - The \( f^{-1}(f(x))=x \) for all x in the domain of f . - The \( f\left(f^{-1}(x)\right)=x \) for all x in the domain of \( f^{-1} \). c. Using graphing paper, sketch the graph which is reflected at \( \mathrm{y}=\mathrm{x} \) using the domain \( -5,-3,-1,0,1,3,5 \). 1. \( f(x)=\frac{x+1}{2} \) 2. \( f(x)=x-5 \) 3. \( f(x)=\sqrt{x-6} \)

d) \( \sqrt{(-7)^{2}}+\sqrt{\frac{25}{16}}-\frac{3}{2} \) e, \( \frac{1}{2} \cdot \sqrt{100}-\sqrt{\frac{1}{6}}+\left(\frac{1}{3}\right)^{0} \)

Write the sentence as an equation. m times 104, decreased by 233 equals 106

Write the inequality using interval notation and illustrate the inequality using the real number line. \( -3 \leq x<7 \) The inequality represents the interval (Type your answer in interval notation.)

Exponential Growth and Decay 1. The population of a city is 810000 . If it is increasing by \( 4 \% \) per year, estimate the population in (foutyears.

Rationalize the denominator of the given expression. \[ \frac{\sqrt{7}}{5-\sqrt{5}} \] \( \frac{\sqrt{7}}{5-\sqrt{5}}= \)