The number 6 is in the domain of fºg.
How to determine the true statement?
The functions are given as:
f(x) = 6x - 9
g(x) = x + 6
The composite function f o g is calculated as:
(f o g)(x) = f(x) * g(x)
This gives
(f o g)(x) = (6x - 9) * (x + 6)
Expand
(f o g)(x) = 6x^2 + 36x - 9x - 54
Evaluate
(f o g)(x) = 6x^2 + 27x - 54
The above function is a quadratic function, and it can take any real number as its input
Hence, 6 is in the domain of fºg.
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