Question

Functions and their PropertiesPracticeNeed help​

Answer 1

Answer:

$g(n-7)=\frac{n^{2}-14n+43}{7n-49}$  → (a)

Step-by-step explanation:

We need to evaluate g(n - 7), where

• $g(x)=\frac{x^{2}-7}{7x}$

Replace x by (n - 7) to evaluate it

∵ x = (n - 7)

∴ $g(n-7)=\frac{(n-7)^{2}-6}{7(n-7)}$

→ Let us find (n - 7)²

∵ (n - 7)² = (n - 7)(n - 7) = (n)(n) + (n)(-7) + (-7)(n) + (-7)(-7)

∴ (n - 7)² = n² + (-7n) + (-7n) + 49 = n² + -14n + 49

∴ (n - 7)² = n² - 14n + 49

→ Find 7(n - 7)

∵ 7(n - 7) = 7(n) - 7(7)

∴ 7(n - 7) = 7n - 49

→ Now let us write then in the form above

∵ $g(n-7)=\frac{n^{2}-14n+49-6}{7n-49}$

→ Add the like terms in the numerator

∴  $g(n-7)=\frac{n^{2}-14n+43}{7n-49}$

The correct answer is (a)