Final answer:
The statement '4 is not in the domain of fºg' is true.
Step-by-step explanation:
To find the domain of fºg, we need to find the values of x for which the composition of the functions is defined. In this case, fºg means applying g(x) to the input of f(x). So, we substitute g(x) into f(x) for the expression f(g(x)).
To do this, substitute √x – 7 for x in f(x) = -5x – 1.
f(g(x)) = -5(√x – 7) – 1
Now we need to find the values of x for which this expression is defined. The square root function (√x) is defined only for non-negative values of x. So, we need to find the values of x that make √x – 7 non-negative.
To do this, set √x – 7 ≥ 0 and solve for x:
√x – 7 ≥ 0
√x ≥ 7
Squaring both sides:
x ≥ 49
So, any value of x greater than or equal to 49 will be in the domain of fºg. Answer choice B is correct.