Know You're Function

Algebra Level 1

If $f(x)=x^{2}+4x+4$
$g(x)=x-2$ and
$h(x)=x^{2}-4x+4$ ,
what would be $f(g(h(0)))$ ?

The answer is 16.

2 solutions

Deutch Mark Dela Rosa
Jul 29, 2014

It's says if x=0

substitute first x as 0 in h(x) where the equation is h(x)=x^2+4x+4

h(x)=x^2+4x+4

h(0)=0^2+4(0)+4

=4

hence, h(x)=4

then substitute h(x) as x of g(x)

g(x)=x-2

g(4)=h(x)-2

   =4-2

   =2

hence, g(x)=2

again substitute g(x) as x in f(x)

f(x)=x^2+4x+4

f(2)=2^2+4(2)+4

   =4+8+4

   =16

then f{g[h(x)]}, if x=0, is equal to 16

Nice approach!!!!

VAIBHAV borale - 6 years, 10 months ago

You probably meant "Your Function" rather than "You're Function," which would imply that the reader should know that he/she is a function. You may want to fix the title.

Marta Reece - 3 years, 6 months ago

Tom Engelsman
Oct 18, 2016

Upon observation:

f(x) = (x + 2)^2; g(x) = x - 2; h(x) = (x - 2)^2

so now we obtain:

g(h(x)) = (x - 2)^2 - 2

and f(g(h(x))) = [(x - 2)^2 - 2 + 2]^2 = (x - 2)^4.

Hence, f(g(h(0))) = (- 2)^4 = 16.

Know You're Function

The answer is 16.

2 solutions

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