Enough Functions for Today

Algebra Level 1

If f f is a function such that f ( f ( x ) ) = x 2 − 1 f(f(x)) = x^2 - 1 , what is the value of f ( f ( f ( f ( 3 ) ) ) ) f(f(f(f(3)))) ?


The answer is 63.

View wiki
Júlian Rikki Réyes by Júlian Rikki Réyes , 20, Philippines

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.

4 solutions

As f ( f ( x ) ) = x 2 − 1 , f(f(x)) = x^2 - 1, f ( f ( f ( f ( 3 ) ) ) ) f(f(f(f(3)))) can be calculated by finding ( f ( 3 ) ) (f(3)) and doing the same for the result.

That is, f ( f ( 3 ) ) = 3 2 − 1 = 8 f(f(3)) = 3^2 - 1 = 8 and f ( f ( 8 ) ) = 8 2 − 1 = 63 f(f(8)) = 8^2 - 1 = 63 .

28 Helpful 8 Interesting 7 Brilliant 5 Confused

Is it possible to construct f(x)? I suspect there is no fuction interpreted on the set of real numbers that would satisfy that f(f(x)) = x^2-1

Gorg Vlad - 4 years, 11 months ago

x = 3 is a negative number. So when f approaches x. we have x = 2.

Am Kemplin - 1 month, 2 weeks ago
Curtis Clement
Apr 4, 2015

f ( f ( f ( f ( x ) ) ) ) = ( x 2 − 1 ) 2 − 1 = x 4 − 2 x 2 = x 2 ( x 2 − 2 ) f(f(f(f(x)))) = (x^2 -1)^2 - 1 = x^4 -2x^2 = x^2 (x^2 -2) Let x = 3: ∴ f ( f ( f ( f ( 3 ) ) ) ) = 9 × 7 = 63 \therefore\ f(f(f(f(3)))) = 9 \times\ 7 = \boxed{63}

16 Helpful 0 Interesting 1 Brilliant 0 Confused
Betty BellaItalia
Apr 17, 2017

2 Helpful 0 Interesting 1 Brilliant 0 Confused
Bruno Martel
Apr 21, 2021

There are 2 ways I believe, get the whole expression (quartic(x)+2x) and replace, or grab groups of the 2 defined equation and replace in the first one and put the result in the second one

0 Helpful 0 Interesting 0 Brilliant 0 Confused

1 pending report

Vote up reports you agree with

×

Problem Loading...

Note Loading...

Set Loading...