Inverse functions
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.
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
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.
Consider the function
g={(-9,2),(0,5),(1,3),(3,-4),(4,9)}
Find g^{-1}(3)=
g^{-1}(3)=1
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)
When (year) did Mexico start their Independence?
1810
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)
*View link*
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
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)
Suppose that the function f(x) is defined as follows: *view link*
Is the function continuous?
It is not continuous. *View link*
Who is Taylor Swift engaged to and which team does he play for?
Travis Kelce - Kansas City Chiefs
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)
Suppose that the function f(x) is defined as follows: *view link*
Is the function continuous?
It is continuous.
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