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If f(x) = cosx g(x) = x^2 find a if f(g(a)) = 1
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Now are given that f(x) = cos x and g(x) = x^2.
If f(g(a)) = 1
=> f( a^2) = 1
=> cos a^2 = 1
=> a^2 = arc cos 1
=> a^2 = 0
=> a = 0
Therefore a is equal to zero.
Posted by justaguide on December 4, 2010 at 1:13 PM (Answer #1)
High School Teacher
Given the functions:
f(x) = cosx.
g(x) = x^2.
We need to determine the value of (a) such that f(g(a)) = 1
First, let us determine the function f(g(x)).
f(g(x)) = f( x^2)
==> f(g(x)) = cos(x^2).
Now we will substitute with x = a.
==> f(g(a)) = cos(a^2)
But, given that f(g(a)) = 1
==> f(g(a)) = cos(a^2) = 1
Then a^2 = 0
==> a= 0.
Then the value of a is 0.
Posted by hala718 on December 4, 2010 at 1:12 PM (Answer #2)
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
a = 0
Posted by giorgiana1976 on December 4, 2010 at 4:32 PM (Answer #3)
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