I'm back! says f ( x ) f(x)

Algebra Level 4

Find the domain of f ( x ) = 1 − 2 − 3 − x f(x) = \sqrt{1-\sqrt{2-\sqrt{3-x}}} .

( 3 , 2 ) (3,2) [ 1 , 2 ] [1,2] [ 2 , − 1 ) [2,-1) ( − 1 , 2 ) (-1,2) [ − 1 , 2 ] [-1,2] ϕ \phi [ 2 , − 1 ] [2,-1] ( 0 , 2 ] (0,2]

A Former Brilliant Member by A Former Brilliant Member

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

J D
May 8, 2016

For f(x) to exist, what is under the root can't be negative. This means that 1-root(2-root(3-x)) is greater than or equal to zero, which means that root(2-root(3-x)) is between zero and one (because a positive square root can't be negative). This means that 2-root(3-x) is between zero and one, which means that root(3-x) is between one and two. This means that 3-x is between one and four, which gives the final answer that the domain is [-1,2] (inclusive because the square root of zero is defined.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...