Question

Функция задана формулой f(x)=x2-4 Найдите f(-3),f(0). Найдиье значение х , при который : f(x)-5;f(x)-0

Answer 1

Ответ:

f(x)=x²-4

1) f(-3)=(-3)²-4=9-4= 5

2) f(0)=0²-4=0-4= -4

3) f(x)=5, x=?

x²-4=5

x²=9

x=±3

4) f(x)=0, x=?

x²-4=0

x²=4

x=±2

Answer 2

To find the values of the function for specific inputs and the value of x for which f(x) equals a given number, let's proceed step by step:

1. Find f(-3) and f(0): Given function f(x) = x^2 - 4

a) f(-3): f(-3) = (-3)^2 - 4 f(-3) = 9 - 4 f(-3) = 5

b) f(0): f(0) = (0)^2 - 4 f(0) = 0 - 4 f(0) = -4

So, f(-3) = 5 and f(0) = -4.

2. Find the values of x for which f(x) equals a given number:

a) f(x) - 5: To find the x-value for which f(x) - 5 = 0, we set f(x) equal to 5 and solve for x:

x^2 - 4 - 5 = 0 x^2 - 9 = 0

Now, we factor the equation:

(x - 3)(x + 3) = 0

Setting each factor to zero and solving for x:

x - 3 = 0 -> x = 3 x + 3 = 0 -> x = -3

So, when f(x) - 5 = 0, x can be either 3 or -3.

b) f(x) - 0: To find the x-value for which f(x) - 0 = 0 (which is just f(x) = 0), we set f(x) equal to 0 and solve for x:

x^2 - 4 = 0

Now, we factor the equation:

(x - 2)(x + 2) = 0

Setting each factor to zero and solving for x:

x - 2 = 0 -> x = 2 x + 2 = 0 -> x = -2

So, when f(x) - 0 = 0, x can be either 2 or -2.

In summary:

• f(-3) = 5
• f(0) = -4
• For f(x) - 5 = 0, x can be 3 or -3.
• For f(x) - 0 = 0, x can be 2 or -2.