Properties of inverse functions Theorem Suppose f and g are

Properties of inverse functions Theorem: Suppose f and g are inverse functions. The range of f is the domain of g and domain of f is the range of g. f(a) = b if and only if g(b) = a. (a, b) is on the graph of f if and only if (b, a) is the graph of g. The function f(x) = x^3 + 3x +1 is one-to-one. Since finding a formula for its inverse is beyond the scope of this textbook, use properties of inverse functions. Theorem to help you compute f^-1 (1), f^-1(5), and f^-1(-3). f^-1(1) = ____ f^-1(5) = ______ f^-1(-3) = ______

Solution

f^-1(1) :
Plug in y = 1 and find x...
x^3 + 3x + 1 = 1
x^3 + 3x = 0
x(x^2 + 3) = 0
x = 0

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f^-1(5) :
5 = x^3 + 3x + 1
x^3 + 3x - 4 = 0

Clearly 1 works for x

So, 1 ---> ANSWER

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-3 = x^3 + 3x + 1

x^3 + 3x + 4 = 0

x = -1 works clearly

-1 ----> ANSWER