Double repeated functions

Algebra Level 1

Let $f(x) = 2x-6$ . Find the value of $x$ for which $f^2(x) = 2$ .

Note: $f^2(x) = f(f(x))$ , NOT $(f(x))^2$ .

2 solutions

Noel Lo
May 6, 2015

$f^2(x) = 2$

$f(2x-6) = 2$

$2(2x-6) - 6 = 2$

$4x-18=2$

$4x = 20$

$x=\boxed{5}$

Otto Bretscher
May 6, 2015

Write the inverse, $x=g(y)=\frac{y+6}{2}$ . Now $x=g(g(2))=g(4)=\boxed{5}.$

U mean $\frac{2+6}{2} = \frac{8}{2} = 4$ and then $\frac{4+6}{2} = \frac{10}{2} =\boxed{5}$ .

Noel Lo - 6 years, 1 month ago

Yes, indeed....those are $g(2)$ and $g(4)$

Otto Bretscher - 6 years, 1 month ago

You can also double check your answer this way:

$f^2(5) = f(f(5)) = f(2(5) - 6) = f(10-6) = f(4)$

$f(4) = 2(4) - 6 = 8-6 = 2$

Noel Lo - 6 years, 1 month ago

Is it not necessary to prove that the inverse of f(x) exists?

Devendra Kumar Singh - 5 years, 8 months ago