<span>
f(x)= −3/5x³</span><span>
The domain is all values x can be. There are no restrictions on x. it can be any real number (-∞ , ∞)
The range is all values y can be. There are noi restrictions on y either because the function is odd. y is </span><span>(-∞ , ∞)
The best answer is D.
domain (-∞, 0] ∪[0, ∞)
range </span><span>(-∞, 0] ∪[0, ∞) </span>
Answer:
-5 ; 1/2
Step-by-step explanation:
<u>GIVEN :-</u>
- A quadratic polynomial f(x) = 2x² + 9x - 5
<u>TO FIND :-</u>
- Zeroes of f(x) = 2x² + 9x - 5
<u>GENERAL CONCEPTS TO BE USED IN THIS QUESTION :-</u>
Lets say there's a quadratic polynomial f(x) = ax² + bx + c , whose factors are (x - α) & (x - β). To find the values of x for which f(x) will be zero , equate the factors of f(x) with 0.
⇒ (x - α) = 0 & (x - β) = 0
⇒ x = α & x = β
Hence, it can be concluded that if (x - α) & (x - β) are factors of f(x) , then α & β are the roots of f(x).
<u>SOLUTION :-</u>
Factorise f(x) = 2x² + 9x - 5.
![=> 2x^2 + 10x - x - 5](https://tex.z-dn.net/?f=%3D%3E%202x%5E2%20%2B%2010x%20-%20x%20-%205)
- Take '2x' common from first two terms & '-1' from last two terms.
![=> 2x(x + 5) - 1(x + 5)](https://tex.z-dn.net/?f=%3D%3E%202x%28x%20%2B%205%29%20-%201%28x%20%2B%205%29)
- Take (x + 5) common from the whole expression.
![=> (x + 5)(2x - 1)](https://tex.z-dn.net/?f=%3D%3E%20%28x%20%2B%205%29%282x%20-%201%29)
So , the factors of f(x) are (x + 5) & (2x - 1). Now equate the factors with zero.
⇒ (x + 5) = 0 & (2x - 1) = 0
⇒ x = -5 & x = 1/2
∴ The zeroes of f(x) = 2x² + 9x - 5 are (-5) & (1/2)
<u>VERIFICATION :-</u>
1) Put x = -5 in f(x) = 2x² + 9x - 5
⇒ f(-5) = 2(-5)² + 9×(-5) - 5
= 50 - 45 - 5
= 50 - 50
= 0
2) Put x = 1/2 in f(x) = 2x² + 9x - 5
![f(\frac{1}{2} ) = 2 \times (\frac{1}{2} )^2 + 9 \times \frac{1}{2} - 5](https://tex.z-dn.net/?f=f%28%5Cfrac%7B1%7D%7B2%7D%20%29%20%3D%202%20%5Ctimes%20%28%5Cfrac%7B1%7D%7B2%7D%20%29%5E2%20%2B%209%20%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%20%20-%205)
![= \frac{1}{2} + \frac{9}{2} - 5](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2B%20%5Cfrac%7B9%7D%7B2%7D%20-%205)
![= \frac{ 1 + 9 - 10}{2}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%201%20%2B%209%20-%2010%7D%7B2%7D)
![= \frac{0}{2}](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B0%7D%7B2%7D)
![= 0](https://tex.z-dn.net/?f=%3D%200)
Answer:
Step-by-step explanation:
Answer:D?
Step-by-step explanation:
Answer:
1. ecosystem
2. ecology
3. biosphere
4. forest
5. outside
Step-by-step explanation: