(a) f(x) = x - 3 → f(-2)

(b) g(x) = x² - 3x + 5 → g(1)

(c) h(x) = √(x³ + x + 6) → h(3)

(d) p(x) = (x² + 1) / (x - 4) → p(5)

Let's evaluate each of the given functions step-by-step:
(a) f(x) = x - 3 \rightarrow f(-2)
To find f ( − 2 ) , substitute − 2 for x in the function:
f ( − 2 ) = − 2 − 3 = − 5
So, f ( − 2 ) = − 5 .
(b) g(x) = x^2 - 3x + 5 \rightarrow g(1)
To find g ( 1 ) , substitute 1 for x in the function:
g ( 1 ) = ( 1 ) 2 − 3 × 1 + 5 g ( 1 ) = 1 − 3 + 5 g ( 1 ) = 3
So, g ( 1 ) = 3 .
(c) h(x) = \sqrt{x^3 + x + 6} \rightarrow h(3)
To find h ( 3 ) , substitute 3 for x in the function:
h ( 3 ) = ( 3 ) 3 + 3 + 6 ​ h ( 3 ) = 27 + 3 + 6 ​ h ( 3 ) = 36 ​ h ( 3 ) = 6
So, h ( 3 ) = 6 .
(d) p(x) = \frac{x^2 + 1}{x - 4} \rightarrow p(5)
To find p ( 5 ) , substitute 5 for x in the function:
p ( 5 ) = 5 − 4 5 2 + 1 ​ p ( 5 ) = 1 25 + 1 ​ p ( 5 ) = 1 26 ​ p ( 5 ) = 26
So, p ( 5 ) = 26 .
These calculations provide the values for each function at the given points.

Answered by OliviaLunaGracy | 2025-07-06