Year 12s: what will be the first way you research your future options? >>

Inverse Function Question?

Suppose that f is a one-to-one function satisfying f(3) = 2, f(2) = 1, f′(2) = 3 and f′(3) = 4. Define a function G by G(x) = f(x)^2/ f^−1(x). Compute G′(2).

So far, I've written:

•

f(3)=2 so f^-1 (2)=3

•

f(2)=1 so f^-1 (1)=2

•

G(x)= 2^2/3 = 4/3

•

G(x)= 1^2/2 = 1/2

But I don't know how to work out f(2) = ? when f'(2)=3.

Reply 1

james22

Your second 2 bullet points don't make sense. G(x) is a function not a fixed number. You need to first differentiate G, and write G' in terms of f.

Reply 2

username970964

Ok, now I see, differentiating G(x), I got G'(x)=2f(x)x/f^-1(x)^0(x). Is that right? Then I subbed in the values from the first 2 bullet points and the 2 from G'(2) and got G'(2) = 4 and G'(2) = 2.

But how do you work out f(2) = ? when f'(2)=3.