1. Sea \( f: \operatorname{Dom}(f) \longrightarrow \mathbb{R} \) la función definida por \[ f(x)=3+\sqrt{x-2} . \] a) Hallar analíticamente \( \operatorname{Dom}(f) \) e \( \operatorname{Im}(f) \) b) Hallar \( A \) y \( B \), subconjuntos de \( \mathbb{R} \), tales que \( f: A \longrightarrow B \) sea biyectiva, justificando su elección. Determinar la fórmula de la función inversa de \( f \), indicando su dominio y codominio.

V. The number of bacteria in a crop is represented by: \( f(t)=3(4)^{t} \), where \( t \) is measured in hours and \( f(t) \) in thousands. 1. What is the initial number of bacteria? 2. How many are they at 20 minutes? 3. How many are they in half an hour? 4. How many are they after \( 2 \frac{1}{2} \) hours?

Part 2 of 5 A campground owner has 2500 m of fencing. He wants to enclose a rectangular field bordering a river, with no fencing along the river. (See the s 0.71 of 1 (a) Write an expression for the length of the field as a function of \( x \). (b) Find the area of the field (area \( = \) length \( \times \) width) as a function of \( x \). (c) Find the value of \( x \) leading to the maximum area. (d) Find the maximum area. (a) \( \ell(x)=2500-2 x \) (b) \( A(x)= \)

When the function \( f(x)=\cos x \) is reflected across the \( x \)-axis, the resulting function is \( g(x)=-\cos x \). If the coordinates of the \( y \)-intercept of \( f(x)=\cos x \) are \( (0,1) \), what are the coordinates of the \( y \)-intercept of the reflected function \( g(x) \) ? (1 point) \( (1,0) \) \( (-1,0) \) \( (0,-1) \) \( (-1,1) \)

Convert \( 195^{\circ} \) to radians.

The table contains values for \( f(x) \). If \( h(x) \) is the reflection of \( f(x) \) across the \( x \)-axis, find the missing value in the ordered pair below, for \( h(x) \). \( x \quad-\frac{\pi}{2}-\frac{\pi}{4} \) \( f(x) \) 0