Solução_Calculo_Stewart_6e

F.
TX.10
34 ¤ CHAPTER 1 FUNCTIONS AND MODELS
(c) (d) (e)
(f ) (g) (h)
9. (a) The domain of f + g is the intersection of the domain of f and the domain of g;thatis,A ∩ B.
(b) The domain of fg is also A ∩ B.
(c) The domain of f/g must exclude values of x that make g equal to 0;thatis,{x ∈ A ∩ B | g(x) 6= 0}.
10. Given two functions f and g,thecomposite function f ◦ g is defined by (f ◦ g)(x) =f(g (x)). The domain of f ◦ g is the
set of all x in the domain of g such that g(x) is in the domain of f.
11. (a) If the graph of f is shifted 2 units upward, its equation becomes y = f(x)+2.
(b) If the graph of f is shifted 2 units downward, its equation becomes y = f(x) − 2.
(c) If the graph of f is shifted 2 units to the right, its equation becomes y = f(x − 2).
(d) If the graph of f is shifted 2 units to the left, its equation becomes y = f(x +2).
(e) If the graph of f is reflected about the x-axis, its equation becomes y = −f(x).
(f ) If the graph of f is reflected about the y-axis, its equation becomes y = f(−x).
(g) If the graph of f isstretchedverticallybyafactorof2, its equation becomes y =2f(x).
(h) If the graph of f is shrunk vertically by a factor of 2, its equation becomes y = 1 2 f(x).
(i) If the graph of f is stretched horizontally by a factor of 2, its equation becomes y = f 1
2 x .
(j) If the graph of f is shrunk horizontally by a factor of 2, its equation becomes y = f(2x).
12. (a) A function f is called a one-to-one function if it never takes on the same value twice; that is, if f(x 1 ) 6=f(x 2 ) whenever
x 1 6=x 2 .(Or,f is 1-1 if each output corresponds to only one input.)
once.
Use the Horizontal Line Test: A function is one-to-one if and only if no horizontal line intersects its graph more than
(b) If f is a one-to-one function with domain A and range B,thenitsinverse function f −1 has domain B and range A and is
defined by
f −1 (y) =x ⇔ f(x) =y
for any y in B. The graph of f −1 is obtained by reflecting the graph of f about the line y = x.