given F(x) = x^3 and G(x) = 2x +4?

Question

find:

a) G^-1 (x)

b) (G . F) (x) (the g times f)

c) F + G

Answer 1

Peter got b and c right, but a is wrong.

G^-1 (x) does not mean square root - it means the inverse of the function.

The inverse of a function is such that f(f-1(x)) = f-1(f(x)) = x.

To find the inverse of a function, do the following:
G(x) = 2x + 4
let y = G(x), then solve so that x = a function of y.
y = 2x + 4
y - 4 = 2x
(y - 4)/2 = x = G-1(x) (solution)

Answer 2

a) ^-1 means sqrt, so its sqrt(2x+4)
b) x^3(2x+4) = 2(x^4) + 4(x^3)
c) x^3 + 2x + 4