Respuesta :
To simplify the expression (49x^(-5))/(7+3x^10x^(-9)), we can follow these steps:
1. Simplify the exponents:
- For the numerator, x^(-5) can be rewritten as 1/x^5.
- For the denominator, x^(-9) can be rewritten as 1/x^9.
The expression becomes (49/x^5)/(7 + 3x^10/x^9).
2. Multiply the numerator and denominator by x^5 to eliminate the negative exponent in the numerator:
[(49/x^5)*(x^5)] / [(7 + 3x^10/x^9)*(x^5)].
This simplifies to (49)/(7x^5 + 3x^5/x^4).
3. Combine the terms in the denominator:
(49)/(7x^5 + 3x).
Now we have simplified the expression to (49)/(7x^5 + 3x), where x is not equal to 0.
Now let's move on to the questions:
a. Find each of the following:
i. g(0): Since the expression involves x in the denominator, the function is undefined for x = 0. Therefore, g(0) is undefined.
ii. g(-1): Substitute x = -1 into the simplified expression:
g(-1) = 49/(7(-1)^5 + 3(-1)) = 49/(7 - 3) = 49/4 = 12.25.
iii. a when g(a) = -2: Substitute g(a) = -2 into the simplified expression and solve for a:
-2 = 49/(7a^5 + 3a).
Solve this equation for a using algebraic methods or numerical methods.
iv. Solve g(a) = 0: Substitute g(a) = 0 into the simplified expression and solve for a:
0 = 49/(7a^5 + 3a).
Solve this equation for a using algebraic methods or numerical methods.
b. List the domain and range of the function:
Domain: The function is defined for all values of x except x = 0, as division by zero is undefined.
Therefore, the domain of the function is all real numbers except x = 0.
Range: The range of the function depends on the values of x. Without further information, it is difficult to determine the exact range.Answer:
Step-by-step explanation:
