Question

Дана функция f(x)=kx+l известно, что f(3)=4 f(4)=3. Найдите k и l

Answer 1

Получаем систему уравнений
{3k+l=4
{4k+l=3
3k+l-4k-l=4-3
-k=1|×(-1)
k=-1
3k+l=4
3×(-1)+l=4
-3+l=4
l=4+3
l=7
f(x)=kx+l
f(x)=(-1)x+7

f(x)=-x+7

f(3)=-3+7
f(3)=4

f(4)=-4+7
f(4)=3

Ответ: f(x)=-x+7

Answer 2

To find the values of k and l, we can use the given information that f(3) = 4 and f(4) = 3.

Given that the function is f(x) = kx + l, we can use these two pieces of information to create a system of equations:

1. For x = 3, f(3) = 4: 4 = k * 3 + l

2. For x = 4, f(4) = 3: 3 = k * 4 + l

Now, we have a system of two equations with two unknowns (k and l). We can solve this system of equations to find the values of k and l.

Let's proceed with the solution:

Step 1: Solve the first equation for l: 4 = 3k + l l = 4 - 3k

Step 2: Substitute the expression for l from Step 1 into the second equation: 3 = k * 4 + (4 - 3k)

Step 3: Simplify the equation: 3 = 4k + 4 - 3k

Step 4: Combine the k terms on the right side: 3 = k + 4

Step 5: Isolate k on one side of the equation: k = 3 - 4 k = -1

Step 6: Now that we have the value of k, we can find the value of l using the expression from Step 1: l = 4 - 3 * (-1) l = 4 + 3 l = 7

So, the values of k and l are: k = -1 l = 7

Therefore, the function is f(x) = -x + 7.