Question

C(x) = 1 + (x₁ / x + x₁ / (x + 3))

(a) Verify that C(x₁) = C(6).

(a) C(3) = C(3) = C(6) = C(6)

corporates

Answer 1

To verify that C(x₁) = C(6), substitute the values into the equation C(x) = 1 + (x₁ / x + x₁ / (x + 3)). Simplifying the equation, we find that C(x₁) is not equal to C(6).

Step-by-step explanation:

To verify that C(x₁) = C(6), we will substitute x = x₁ into the equation C(x) = 1 + (x₁ / x + x₁ / (x + 3)).

C(x₁) = 1 + (x₁ / x₁ + x₁ / (x₁ + 3)).

Simplifying further, C(x₁) = 1 + (1 + 1 / (x₁ + 3)).

Since x₁ = 6, we have C(x₁) = 1 + (1 + 1 / (6 + 3)).

C(x₁) = 1 + (1 + 1 / 9) = 1 + (1 + 1/9) = 1 + (10/9) = 19/9.

Now, we will evaluate C(6) by substituting x = 6 into the equation.

C(6) = 1 + (6 / 6 + 6 / (6 + 3)).

Simplifying further, C(6) = 1 + (6 / 12 + 6 / 9).

Since 12 is divisible by 6 and 9, we can simplify as follows: C(6) = 1 + (1/2 + 2/3).

Combining the fractions, C(6) = 1 + (3/6 + 4/6) = 1 + (7/6) = 13/6.

Therefore, C(x₁) = 19/9 and C(6) = 13/6, so C(x₁) is not equal to C(6).