Given that \(a > 0\), if \(f(g(a)) = 8\), where \(f(x) = x^2 + 8\) and \(g(x) = x^2 - 4\), what is the value of \(a\)?
+57 Given that a > 0, if f(g(a)) = 8, where f(x) = x^2 + 8 and g(x) = x^2 - 4, what is the value of a?
Substitute in g(x)
f(g(a)) = f(a^2 - 4)
f(a^2 - 4) = (a^2 - 4)^2 + 8
We bring that back into the original equation
(a^2 - 4)^2 + 8 = 8
(a^2 - 4)^2 = 0
a^2 - 4 = 0
a^2 = 4, a = 2
Answer: a = 2
Check:
f(0) = 0^2 + 8 = 8
:)
+37146 Given that f( g(a) ) = 8 then the thing in the parentheses must be 0
because g(a)^2 + 8 = 8 then g(a)^2 = 0 g(a) = 0
so g(a) must = 0
0 =a^2-4
a^2 = 4 a = 2 (since we only want positives)
