i-found-some-interesting-basic-question-hence-sharing-1-if-A-1-4-A-2-find-interval-2-if-A-1-4-A-2-3-y-1-A-and-A-1-4-y-4-y-1-A-A-1-4-y-

Question Number 60514 by tanmay last updated on 21/May/19

i f o u n d s o m e i n t e r e s t i n g b a s i c q u e s t i o n

h e n c e s h a r i n g \dots

1) i f A \in [1, 4] A^{2} \in ? \leftarrow f i n d i n t e r v a l

2) i f A \in [- 1, 4] A^{2} \in ?

3) y = \frac{1}{A} a n d A \in [1, 4] y \in ?

4) y = \frac{1}{∣ A ∣} A \in [- 1, 4] y \in ?

Commented by kaivan.ahmadi last updated on 22/May/19

1 . A^{2} \in [1, 16]

2 . A^{2} \in [0, 16]

3 . 1 ⩽ A ⩽ 4 \Rightarrow 1 ⩾ \frac{1}{A} ⩾ \frac{1}{4} \Rightarrow \frac{1}{4} ⩽ y ⩽ 1

4 . i f A \neq 0

- 1 ⩽ A < 0 \Rightarrow 0 <∣ A ∣⩽ 1 \Rightarrow \frac{1}{∣ A ∣} ⩾ 1

0 < A ⩽ 4 \Rightarrow \frac{1}{∣ A ∣} ⩾ \frac{1}{4}

\Rightarrow y ⩾ \frac{1}{4}

Commented by tanmay last updated on 22/May/19

1) l e t A = x a n d y = x^{2}

A \in [1, 4] s o A^{2} \in [1, 16]

2) A \in [- 1, 4] f r o m g r a p h y = x^{2}

m i n i m u m v a l u e o f x^{2} = 0

s o A^{2} \in [0, 16]

Commented by tanmay last updated on 22/May/19

Commented by tanmay last updated on 22/May/19

3) l e t x = A a n d y = \frac{1}{A}

A \in [1, 4] \frac{1}{A} \in [0.25, 1]

Commented by tanmay last updated on 22/May/19

t h a n k y o u s i r

Answered by tanmay last updated on 22/May/19

4) A = x y = \frac{1}{∣ x ∣}

w h e n x = - 1 y = \frac{1}{∣ - 1 ∣} = 1

w h e n x = 4 y = \frac{1}{4}

A \in [- 1, 4]

\frac{1}{[A]} \in [1, \infty) \cap [\frac{1}{4}, \infty)

Commented by tanmay last updated on 22/May/19

Commented by MJS last updated on 22/May/19

[1, \infty) \cap [\frac{1}{4}, \infty) = [1, \infty)

so your conclusion is wrong . the path is ok .

\frac{1}{∣ A ∣} \in [\frac{1}{4}, \infty) is the right answer

Commented by tanmay last updated on 22/May/19

t h a n k y o u s i r \dots

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