Explain, please?

1. Let g(x) is the reflection of f(x) about the line y=x, and f'(x)= x^12/1+x^2, if g(3)=a, then g'(3) =

a) (1+a^2)/a

b) a^12/(1+a^2)

c) (1+a^2)/a^12

d) a/(1+a^2)

1 Answer

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  • 6 months ago

    "Reflection of f(x) about the line y=x" is another way of saying "inverse function of f(x)".  Use the derivative of the inverse formula:

        g(x) = f⁻¹(x)

        g'(x) = d/dx f⁻¹(x) = 1/f'(f⁻¹(x))

        g'(x) = 1 /  f'(g(x))

        g'(3) = 1 / f'(g(3)) = 1/f'(a)

    When I first read the question, I thought there was more than one error in the question, since x^12 doesn't show up in problems very often.  As typed, your function simplifies to f'(x) = [(x^12) / 1] + (x^2) = x^12 + x^2; and none of the answers match 1/f'(a) with that interpretation of f.

    It looks like you forgot parentheses around (1 + x^2) in the expression for f'(x).  That would make (c) the correct answer.

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