In Exercise 53-58, evaluate each piecewise function at the given values of the independent variable, f ( x ) = { 3 x + 5 if x < 0 4 x + 7 if x ≥ 0 a. f ( − 2 ) b. f (0 ) c. f (3)
In Exercise 53-58, evaluate each piecewise function at the given values of the independent variable, f ( x ) = { 3 x + 5 if x < 0 4 x + 7 if x ≥ 0 a. f ( − 2 ) b. f (0 ) c. f (3)
Solution Summary: The author calculates the value of f(-2) in the piecewise function.
In Exercise 53-58, evaluate each piecewise function at the given values of the independent variable,
f
(
x
)
=
{
3
x
+
5
if
x
<
0
4
x
+
7
if
x
≥
0
a.
f
(
−
2
)
b.f (0)
c.f (3)
Definition Definition Group of one or more functions defined at different and non-overlapping domains. The rule of a piecewise function is different for different pieces or portions of the domain.
2. We want to find the inverse of f(x) = (x+3)²
a. On the graph at right, sketch f(x).
(Hint: use what you know about
transformations!) (2 points)
b. What domain should we choose to
get only the part of f (x) that is one-
to-one and non-decreasing? Give
your answer in inequality notation. (2
points)
-
c. Now use algebra to find f¯¹ (x). (2
points)
-4-
3-
2
1
-4
-3
-2
-1
0
1
-1-
-2-
--3-
-4
-N-
2
3
4
1. Suppose f(x) =
2
4
==
x+3
and g(x) = ½-½. Find and fully simplify ƒ(g(x)). Be sure to show all
x
your work, write neatly so your work is easy to follow, and connect your expressions
with equals signs. (4 points)
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