Question

Given: f(x) = x + 2 and g(x) = x2 +3, find the following:

28) f(-3)
29) f(g(2))
30) g(f(x))
31) f-1(x)

Answer 1

28) -1

29) 9

30) x^2+4x+7

31) x-2

Explanation:

Given:

f(x) = x + 2

g(x) = x^2 +3

Find:

28) f(-3)

29) f(g(2))

30) g(f(x))

31) f-1(x)

Solution:

Put the function argument values into the expression and do the arithmetic.

28) f(-3) = (-3) +2 = -1

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29) f(g(2)) = f((2)^2 +3) = f(7) = (7) +2 = 9

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30) g(f(x)) = g(x+2) = (x+2)^2 +3 = x^2 +4x +7

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31) The meaning of y = f^-1(x) is x = f(y).

x = f(y) = y+2

y = x -2

f^-1(x) = x -2