Question

Функция задана формулой f(x) = x² - 9 a) Найдите f(0), f(-4) б) Найдите значения x, при которых f(x) = -8; 0

Answer 1

Ответ:

Объяснение:

1)x = 3;x = квадрат от 5

2)x=1;x=3

Answer 2

To find the values of the function $f(x) = x^2 - 9$, we can plug the given values of $x$ into the function and compute the results.

a) Find $f(0)$ and $f(-4)$: a.1) $f(0)$: $f(0) = 0^2 - 9 = -9.$

a.2) $f(-4)$: $f(-4) = (-4)^2 - 9 = 16 - 9 = 7.$

b) Find the values of $x$ when $f(x) = -8$ and $f(x) = 0$: b.1) For $f(x) = -8$: $-8 = x^2 - 9.$

To find the values of $x$ that satisfy this equation, we'll first bring $9$ to the left-hand side: $x^2 - 9 + 8 = 0.$

Now, combine the constants on the left side: $x^2 - 1 = 0.$

Factor the equation: $(x+1)(x-1) = 0.$

Now, set each factor to zero and solve for $x$: $x + 1 = 0 \Rightarrow x = -1,$ $x - 1 = 0 \Rightarrow x = 1.$

So, $x = -1$ and $x = 1$ are the solutions for $f(x) = -8$.

b.2) For $f(x) = 0$: $0 = x^2 - 9.$

Following the same steps as before, we get: $(x+3)(x-3) = 0.$

Now, set each factor to zero and solve for $x$: $x + 3 = 0 \Rightarrow x = -3,$ $x - 3 = 0 \Rightarrow x = 3.$

So, $x = -3$ and $x = 3$ are the solutions for $f(x) = 0$.