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Home > CALC > Chapter 7 > Lesson 7.3.3 > Problem 7-137

7-137.
  1. Given: f(x) and g(x) continuous and differentiable such that f(g(x)) = x. Homework Help ✎

    Evaluate.

    1. f ′(g(0))

    2. g′(1)

    3. g′(2)

    4. f ′(g(2))

    5. 3 · f ′(2)

    6. 5 · f ′(1) + 6 · g ′(1)

    x

    f(x)

    f ′(x)

    g(x)

    –1

    2

    1

    0

    0

    –1

    2

    2

    1

    1

    7

    1

    2

    0

    3

    –1

Since g(2) = −1,
the inverse, f(−1) = 2.
Now f '(−1) = 1, so g '(2) = __
Refer to the hint in part (b)

Refer to the hint in part (b).

How to find derivative of inverse functions:
A function, f, and its inverse, g, will have reciprocal derivatives at corresponding (x, y)→(y, x) values.