Question

При каких значениях "х" значения функции у=3х-4/5 принадлежат промежутку [0;1] ?

Answer 1

0 ≤ 3x - 4/5 ≤ 1

0 + 4/5 ≤ 3x ≤ 1 + 4/5

0,8 ≤ 3x ≤ 1,8

4/15 ≤ x ≤ 0,6

При x ∈ [4/15 ; 0,6] значения y ∈ [0 , 1]

Answer 2

Т.к. значение функции принадлежит промежутку, мы можем записать так:

$0 \leqslant y \leqslant 1$

Подставим вместо $y$само выражение

$0 \leqslant 3x - \frac{4}{5} \leqslant 1 \\ \frac{4}{5} \leqslant 3x \leqslant \frac{9}{5} \\ \frac{4}{15} \leqslant x \leqslant \frac{9}{15}$

т.е.

$x\in\bigg[\frac{4}{15};\frac{3}5\bigg]$

Answer 3

To find the values of "x" for which the function y = 3x - 4/5 belongs to the interval [0, 1], we need to set up the inequality and solve for "x". The inequality is:

0 ≤ y = 3x - 4/5 ≤ 1

Step 1: Solve the left part of the inequality:

0 ≤ 3x - 4/5

Step 2: Solve the right part of the inequality:

3x - 4/5 ≤ 1

Now, let's solve each part separately.

Step 1:

0 ≤ 3x - 4/5

Add 4/5 to both sides to isolate 3x:

4/5 ≤ 3x

Now, divide both sides by 3:

4/15 ≤ x

Step 2:

3x - 4/5 ≤ 1

Add 4/5 to both sides to isolate 3x:

3x ≤ 9/5

Now, divide both sides by 3:

x ≤ 3/5

Now that we have both parts of the inequality solved, we need to find the intersection of the two solutions. The values of "x" that satisfy the original inequality are those that make both conditions true. So, we look for the overlapping interval:

4/15 ≤ x ≤ 3/5

Hence, the values of "x" for which the function y = 3x - 4/5 belongs to the interval [0, 1] are given by:

4/15 ≤ x ≤ 3/5