Study Flashcards
(35 cards)
The domain of f+g, f-g, and fg is the
Intersection of the domain of f and g
The domain of a composite function (f ○ g) is the set of x such that
g(x) is defined and is in the domain of f
g(x) is defined and is in the domain of f
The domain of a composite function (f ○ g) is the set of x such that
Break down 1/√2x^2+1
f(1)(x)=x^2
f(2)(x)=2x
f(3)(x)=+1
f(4)(x)= √x
f(5)(x)=1/x
f(1)(x)=x^2
f(2)(x)=2x
f(3)(x)=+1
f(4)(x)= √x
f(5)(x)=1/x
Break down 1/√2x^2+1
A function is one-to-one if
f(x1)=f(x2) implies x1=x2 for all x, and x2 is in the domain of f.
f(x1)=f(x2) implies x1=x2 for all x, and x2 is in the domain of f.
One-to-one function
A function is one-to-one if its graph
Passes the horizontal line test
Passes the horizontal line test
One-to-one function
How do you algebraically determine one-to-one functions?
Set it equal to itself and see if it comes out the same
Set it equal to itself and see if it comes out the same
Algebraically determine one-to-one functions
Let f be one-to-one. The inverse of f is is the function f^-1 defined by
x=f^-1(x) iff y=f(x)
x=f^-1(x) iff y=f(x)
The inverse of f is is the function f^-1 defined by
f^-1(f(x))=x for all
x in the domain of f
f(f^-1(x))=x for all
x in the domain of f^-1
How do you show that functions are inverses?
If f(g(x))=x
If f(g(x))=x
Inverse functions
Quadratic function form
f(x)=ax^2+bx+c where a,b,c are in R and a≠0
f(x)=ax^2+bx+c where a,b,c are in R and a≠0
Quadratic function form
Standard (vertex) form where (h,k) is vertex
a(x-h)^2+k
a(x-h)^2+k
Standard (vertex) form where (h,k) is vertex
The graph of every quadratic function is
A parabola
A parabola is every
Quadratic function
(h,k) is absolute global minimum of f if
F opens upward
