# 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

- husoskiLv 76 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.