Question

ܕ
957 Which of the following is NOT in the range of f(x)
1-lx
A ?
8. 1.5
1
D. 0.5​

Answer 1

Question: Which of the following is NOT in the range of f(x) = 1/(1 - lxl).

A.2, B.1.5 C.1 D.0.5

Answer:

0.5

Step-by-step explanation:

Let f(x) = y → y = 1/(1 - |x|)

=> 1 - |x| = 1/y → |x| = 1 - 1/y

As |x| will always be a positive number, it will always be greater than 0, or 0 itself.

=> 0 ≤ 1 - 1/y => 1/y ≤ 1

=> y ≤ y² (multiply both sides by y²)

=> 0 ≤ y(y - 1)

This is possible when (- ∞, 0) U [1, ∞)

Notice that 0.5 doesn't belong to (- ∞, 0) U [1, ∞)

Answer 2

Answer:

Let f(x) = y → y = 1/(1 - |x|)

=> 1 - |x| = 1/y → |x| = 1 - 1/y

As |x| will always be a positive number, it will always be greater than 0, or 0 itself.

=> 0 ≤ 1 - 1/y => 1/y ≤ 1

=> y ≤ y² (multiply both sides by y²)

=> 0 ≤ y(y - 1)

This is possible when (- ∞, 0) U [1, ∞)

Notice that 0.5 doesn't belong to (- ∞, 0) U [1, ∞)