a. Graph f ( x ) = x 2 + 1 ; x ≤ 0 . 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 + 1 ; x ≤ 0 . 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 how the graph of f(x)=x2+1;x 0 is given by b.
a. Graph
f
(
x
)
=
x
2
+
1
;
x
≤
0
. 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.
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