If f(x)=5x+7 and g(x)=√x+6, which statement is true?

a.) 9 is not in the domain of f ° g
b.) 9 is in the domain of f ° g

Statement b is true; statement a is false

Step-by-step explanation:

Best to write out (f o g)(x) and then determine its domain:

"(f o g)(x)" indicates that g(x) is used as the input to f(x):

(f o g)(x) = 5(√x+6) + 7, or 5√x + 30 + 7, or 5√x + 37.

The domain of this composite function is [0, infinity).

Thus, statement b is true:  "9 is part of the domain of (f o g)(x) = 5(√x+6) + 7"

step-by-step explanation:

to determine whether a given function is even, we simply substitute x with -x in the expression. if the result after simplification is identical to the original equation, then the function is said to be even other wise odd.

f(-x) = (-x)^2 - (-x) + 8

      = x^2 + x +8

the resulting function is not identical to the original one;

f(-x) ≠ f(x)

therefore, f(x) is not an even function