If f(x) = cosx g(x) = x^2 find a if f(g(a)) = 1

To determine the value of a, we'll have to determine first
the composition of the given functions f and g.

f(g(x)) is
the result of composing f and g:

(fog)(x) =
f(g(x))

To determine the expression of the composed
function, we'll substitute x by g(x) and we'll get:

f(g(x))
= cos g(x)

Now, we'll substitute g(x) by it's
expression:

f(g(x)) = cos
x^2

Since we know the expression of f(g(x)), we can
determine f(g(a)):

f(g(a)) = cos
a^2

But, from enunciation, f(g(a)) = 1,
so:

cos a^2 = 1

a^2 =
+/-arccos 1 + 2*k*pi

a^2 = 0 +
2*k*pi

a = +/-sqrt
2kpi

or

a
= 0