julielebo8
21.11.2020 •
Mathematics
3. Functions f, g, and h are defined as follows: f(x) = x + 1, g(x) = x2 +1, and h(x) = x + 1. (a) Find the inverse of function g(x). (b) Find f(h(-2)). (c) Find g(f(3)).
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Ответ:
9514 1404 393
(a) g^-1(x) = ±√(x -1)
(b) 0
(c) 17
Step-by-step explanation:
(a) The inverse is found by solving for y:
x = g(y)
x = y² +1
x -1 = y² . . . . . . subtract 1
y = ±√(x-1) . . . . take the square root
g^-1(x) = ±√(x -1) . . . . in functional form
Note: the inverse of g(x) is not a function, because it is double-valued.
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(b) f(h(-2)) = f(-2+1) = f(-1) = f(-1+1)
f(h(-2)) = 0
__
(c) g(f(3)) = g(3+1) = g(4) = 4² +1
g(f(3)) = 17
Ответ: