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If f(x) = x2 and g(x) = x + 6, find g(f(0)).
Solution:
To determine the function g(f(0)) we need to determine g(f(x)).
g(f(x) is a composite function where g(x) takes the input as the output of f(x).
For that the variable x in function g(x) is replaced by f(x).
g(f(x)) = g(x2 )
g(x2) = x2 + 6
g(f(0)) = (0)2 + 6
= 0 + 6
= 6
Another example could be: If f(x) = x2 + 2x + 5 and g(x) = x + 6, find g(f(0)).
To determine the function g(f(0)) we need to determine g(f(x)).
For that the variable x in function g(x) is replaced by f(x).
g(f(x)) = x2 + 2x + 5 + 6
= x2 + 2x + 11
g(f(0)) = (0)2 + 2(0) + 11
= 0 + 0 + 11
= 11
If f(x) = x2 and g(x) = x + 6, find g(f(0)).
Summary:
If f(x) = x2 and g(x) = x + 6, then g(f(0)) = 6
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