M2 Inverse and piecewise functions

Inverse functions

100

For the functions: f(x)=-x/3 and g(x)=-3x,

Find f(g(x))=

Find g(f(x))=

¿Are f(x) and g(x) inverses of each other?

f(g(x))=x

g(f(x))=x

f(x) and g(x) are inverses of each other.

200

Consider the function 

g={(-9,2),(0,5),(1,3),(3,-4),(4,9)}

Find g^{-1}(3)=

g^{-1}(3)=1

300

Graph the function connected by the points:

(-6,-4),(0,-3),(2,0),(3,4)

Find and draw the inverse AND the axis of symmetry

(-4,-6), (-3,0), (0,2),(4,3)

400

Consider the function f(x)=sqrt(x+3)-1 for the domain [-3,infinity)

Find the inverse function and the domain.

f^{-1}=(x+1)^2-3 for the domain [-1,infinity)

500

Consider the function f(x)=(3x-2)/(2x+3),

Find the inverse function, the domain and range in interval notation.

f^{-1}(x)=(-3x-2)/(2x-3)

Domain=(-infinity, 3/2)U(3/2, infinity)

Range=(-infinity, -3/2)U(-3/2, infinity)

Piecewise functions

100

Consider the piecewise function f(x): *view link*

Find:

f(-1)=

f(-0.25)=

f(1)=

f(-1)=-1

f(-0.25)=0

f(1)=1

200

Consider the graph: *view link*

Write the domain and range of g as intervals.

Domain: [-5,-2)U(1,3)

Range: (-3,-1)U[0,2)

300

Graph the function h(x) *view link*

*View link*

400

Suppose that the function f(x) is defined as follows: *view link*

Is the function continuous?

It is not continuous. *View link*

500

Suppose that the function f(x) is defined as follows: *view link*

Is the function continuous?

It is continuous.

Random

100

Create a piecewise function (graph and f(x) expression) for your weekend (e.g., hours of sleep, level of energy, time spent studying).

Teacher check.

200

When (year) did Mexico start their Independence?  

1810

300

Scientists have found a relationship between the temperature and the height above the surface. T(h)=38-1.25h is the temperature in Celsius at a height of h km above the planet's surface.

Complete:

a) Which statement best describes T^{-1}?

b) Find T^{-1}:

The height above the surface (in km) when the temperature is x degrees Celsius.

T^{-1}(x)=-(x-38)/1.25

400

Who is Taylor Swift engaged to and which team does he play for?

Travis Kelce - Kansas City Chiefs

500

Write ALL the topics we have learned for the PARCIAL 1 (modules 1 and 2).

Module 1: Function evaluation and operations, and composite functions

Module 2: Inverse and piecewise functions