In problems 43 − 54 , the function f is one-to-one. ( a ) Find its inverse function f − 1 and check your answer. ( b ) Find the domain and range of f and f − 1 . ( c ) Graph f , f − 1 , and y = x on the same coordinate axes. f ( x ) = x 3 2 + 5
In problems 43 − 54 , the function f is one-to-one. ( a ) Find its inverse function f − 1 and check your answer. ( b ) Find the domain and range of f and f − 1 . ( c ) Graph f , f − 1 , and y = x on the same coordinate axes. f ( x ) = x 3 2 + 5
Solution Summary: The author explains how to determine the inverse function f-1 and check the answer.
In problems
43
−
54
,
the function
f
is one-to-one.
(
a
)
Find its inverse function
f
−
1
and check your answer.
(
b
)
Find the domain and range of
f
and
f
−
1
.
(
c
)
Graph
f
,
f
−
1
,
and
y
=
x
on the same coordinate axes.
Consider the function f(x) = x²-1.
(a) Find the instantaneous rate of change of f(x) at x=1 using the definition of the derivative.
Show all your steps clearly.
(b) Sketch the graph of f(x) around x = 1. Draw the secant line passing through the points on the
graph where x 1 and x->
1+h (for a small positive value of h, illustrate conceptually). Then,
draw the tangent line to the graph at x=1. Explain how the slope of the tangent line relates to the
value you found in part (a).
(c) In a few sentences, explain what the instantaneous rate of change of f(x) at x = 1 represents in
the context of the graph of f(x). How does the rate of change of this function vary at different
points?
1. The graph of ƒ is given. Use the graph to evaluate each of the following values. If a value does not exist,
state that fact.
и
(a) f'(-5)
(b) f'(-3)
(c) f'(0)
(d) f'(5)
2. Find an equation of the tangent line to the graph of y = g(x) at x = 5 if g(5) = −3 and g'(5)
=
4.
-
3. If an equation of the tangent line to the graph of y = f(x) at the point where x 2 is y = 4x — 5, find ƒ(2)
and f'(2).
Does the series converge or diverge
Chapter 4 Solutions
Mylab Math With Pearson Etext -- 24-month Standalone Access Card -- For Precalculus: Concepts Through Functions, A Unit Circle Approach To Trigonometry, A Corequisite Solution (4th Edition)
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