Final answer:
The student's question involves finding the composite function f(g(x)) by substituting g(x) = 9x² − 7 into f(x) = √(7 + x). After the substitution and simplification, we obtain f(g(x)) = 3x.
Step-by-step explanation:
The question provided by the student seems to require finding the composite function of f(g(x)) involving the two given functions f(x) and g(x). To find f(g(x)), we evaluate f(x) at the point where x equals g(x), hence substituting g(x) into f(x). We begin with the inner function, g(x) = 9x² − 7, and then we substitute this expression for x in the outer function, f(x) = √(7 + x). The result will give us the composite function f(g(x)). Here's a step-by-step process:
- Compute g(x): g(x) = 9x² − 7.
- Replace x in f(x) with g(x): f(g(x)) = √(7 + g(x)).
- Simplify: f(g(x)) = √(7 + (9x² − 7)) = √(9x²).
- Since the square root and the square cancel each other out: f(g(x)) = 3x.
This answer involves concepts such as function composition, square roots which correspond to fractional powers, and the algebraic manipulation of functions.