AP Calculus BC 3.4: Inverse Function Derivatives

Practise AP Calculus BC 3.4 questions by matching inverse-function inputs to function values and applying reciprocal derivative relationships to evaluate inverse derivatives.

Exam points

Use g′(a)=1/f′(g(a)) to evaluate an inverse-function derivative at a specified input.

[Maximum number: 1]

If $f(x)=\sin x+2 x+1$ and g is the inverse function of f, what is the value of $g^{\prime}(1)$ ?

$\frac{1}{3}$

$\frac{1}{2+\cos 1}$

$2+\cos 1$

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FUN-3.E—Calculate derivatives of inverse and inverse trigonometric functions—Topic 3.4 question 1