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

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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