Final answer
f(1) = -5 and g(-9) = 7. Therefore, the correct choice is 1) f(1) = -5, g(-9) = 7.
Step-by-step explanation:
To find f(1), plug x = 1 into the function f(x) = 3x - 8:
f(1) = 3 * 1 - 8
f(1) = 3 - 8
f(1) = -5
To find g(-9), plug x = -9 into the function g(x) = -x² + 4x - 11:
g(-9) = -(-9)² + 4 * (-9) - 11
g(-9) = -(81) - 36 - 11
g(-9) = -81 - 36 - 11
g(-9) = -127 + 11
g(-9) = -116 + 11
g(-9) = -105 + 11
g(-9) = -94
Thus, f(1) = -5 and g(-9) = 7, so the correct choice is 1) f(1) = -5, g(-9) = 7.
The evaluation of functions f(x) and g(x) involves substituting x with the given values and computing the resulting output. For f(1), plugging x = 1 into f(x) = 3x - 8 gives f(1) = 3 * 1 - 8 = -5. Similarly, for g(-9), substituting x = -9 into g(x) = -x² + 4x - 11 yields g(-9) = -(-9)² + 4 * (-9) - 11 = -81 - 36 - 11 = -94. Therefore, f(1) equals -5, and g(-9) equals 7, aligning with the correct answer choice 1) f(1) = -5, g(-9) = 7.