Question

Consider f(x) = 1- x4 (1 - x power 4) Restrict the domain of f(x) so that the restricted function is one-to-one
1. x ≥ 1
2. x ≤ -1
3. x ≥ 0
4. x ≤ 1

Answer 1

Answer:

Let f(x)=2x and g(x)=

x

2

.

Apply the function g to the number 3, and then apply f to the result:

g(3)=

3

2

andf(

3

2

)=3.

A similar thing happens if we first apply f and then apply g:

f(3)=6andg(6)=3.

It is clear that this will happen with any starting number. This is expressed as

f(g(x)) =x,for all x g(f(x)) =x,for all x.

The function f reverses the effect of g, and the function g reverses the effect of f. We say that f and g are inverses of each other.