In Problems 48–51 , the functions f ( x ), g ( x ), and h ( x ) are differentiable for all values of x . Find the derivative of each of the following functions, using symbols such as f ( x ) and f ′( x ) in your answers as necessary. f ( x ) g ( x ) h ( x )
In Problems 48–51 , the functions f ( x ), g ( x ), and h ( x ) are differentiable for all values of x . Find the derivative of each of the following functions, using symbols such as f ( x ) and f ′( x ) in your answers as necessary. f ( x ) g ( x ) h ( x )
In Problems 48–51, the functions f(x), g(x), and h(x) are differentiable for all values of x. Find the derivative of each of the following functions, using symbols such as f(x) and f′(x) in your answers as necessary.
f
(
x
)
g
(
x
)
h
(
x
)
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
In Problems 47–52, find functions f and g so that f ∘ g = H.
In Problems 27–36, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x))
any values of x that need to be excluded.
= x. Give
27. f(x) = 3x + 4; g(x) =
(x- 4)
28. f(x) = 3 – 2x; g(x) = -(x – 3)
29. f(x) = 4x – 8; 8(x) = + 2
30. f(x) = 2x + 6; 8(x) = ;x - 3
31. f(x) = x' - 8; g(x)·
Vx + 8
32. f(x) = (x – 2)², 2; g(x) = Vĩ + 2
33. f(x) = ; 8(x) =
34. f(x) = x; g(x)
x - 5
2x + 3'
2x + 3
4x - 3
3x + 5
35. f(x)
*: 8(x) =
8(x)
36. f(x) =
1- 2x
x + 4
2 - x
1.7
82 CHAPTER 1 Graphs and Functions
In Problems 37-42, the graph of a one-to-one function f is given. Draw the graph of the inverse function f"1. For convenience (and as
a hint), the graph of y = x is also given.
37.
y= X
38.
39.
y =X
3
(1, 2),
(0, 1)
(-1,0)
(2. )
(2, 1)
(1, 0) 3 X
(0, -1)
-3
(-1, -1)
3 X
-3
(-2, -2)
(-2, -2)
-하
-하
-하
40.
41.
y = x
42.
y = X
(-2, 1).
-3
3 X
(1, -1)
In Problems 13–22, for the given functions f and g, find:(a) (f ∘ g) (4) (b) (g ∘ f) (2) (c) (f ∘ f) (1) (d) (g ∘ g) (0)
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