Define for all real

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Define

f(x)=x^{4}-4x^{2}

for all real

x

. Let

S

be the set of real numbers

y

for which

(f^{-1})'(y)

fails to exist. Which statement about

S

is true? (a)

S

contains exactly 3 distinct real numbers. (b)

S

contains exactly 2 distinct real numbers. (c)

S

contains exactly 1 distinct real number. (d)

S

contains infinitely many real numbers.

Related theory

Curve Analysis
Derivatives of Inverse Functions
Advanced Differentiation

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