Composition and Negative Exponents

[goldkat]

Given f(x)=2x+5 and g(x)=x^2 show that f^-1(g^-1(x)) equals {g(f(x)}^-1.

Ive been working at this for hours. I have 1/ 2x^2+5 and 1/ 4x^2+20x+25 so far, what else should I add?

 

[Quaid]

Given f(x)=2x+5 and g(x)=x^2 show that f^-1(g^-1(x)) equals {g(f(x)}^-1.

Ive been working at this for hours. I have 1/ 2x^2+5 and 1/ 4x^2+20x+25 so far, what else should I add?

Hi goldkat:

In this exercise, the ^-1 notation is not an exponent.

f^-1(x) denotes the inverse function of f(x).

y=f(x)

f^-1(y)=x

Does this sound familiar?

You need to determine the inverse functions for f and g, first. Then show that the two given expressions each equal (±√x - 5)/2.

Ciao