a. Graph f x = x − 2 . b. From the graph of f , is f a one-to-one function? c. Write the domain of f in interval notation. d. Write the range of f in interval notation. e. Write an equation for f − 1 x . f. Explain why the restriction x ≥ 0 is placed on f − 1 . g. Graph y = f x and y = f − 1 x on the same coordinate system . h. Write the domain of f − 1 in interval notation. i. Write the range of f − 1 in interval notation.
a. Graph f x = x − 2 . b. From the graph of f , is f a one-to-one function? c. Write the domain of f in interval notation. d. Write the range of f in interval notation. e. Write an equation for f − 1 x . f. Explain why the restriction x ≥ 0 is placed on f − 1 . g. Graph y = f x and y = f − 1 x on the same coordinate system . h. Write the domain of f − 1 in interval notation. i. Write the range of f − 1 in interval notation.
Solution Summary: The author explains that the function f(x)=sqrtx-2 is a one-to-one function.
b. From the graph of
f
, is
f
a one-to-one function?
c. Write the domain of
f
in interval notation.
d. Write the range of
f
in interval notation.
e. Write an equation for
f
−
1
x
.
f. Explain why the restriction
x
≥
0
is placed on
f
−
1
.
g. Graph
y
=
f
x
and
y
=
f
−
1
x
on the same coordinate system.
h. Write the domain of
f
−
1
in interval notation.
i. Write the range of
f
−
1
in interval notation.
System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.
Consider the graphs of y = f(x) and y = g(x) in the given diagram
y= f(x).
y = g(x)
Evaluate (f+g)(2) -5
Determine all for which g(x) < f(x)
Determine all for which f(x) +3 = g(x)
I) For what value(s) of x does g(x) = -4? Separate multiple answers with commas as needed.
J) Give the interval(s) of such that g(x) > 0. Use the union symbol between multiple intervals.
K) Give the interval(s) of such that g(x) <0. Use the union symbol between multiple intervals.
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.