rang of quadratic expression y=x^2+6x-4 and x belong to (-4,3)

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rang of quadratic expression y=x^2+6x-4 and x belong to (-4,3)

Asked by maheshv9090 | 16 Oct, 2023, 09:30: PM

Expert Answer

Given function is

begin mathsize 14px style y left parenthesis x right parenthesis space equals space x squared plus 6 x minus 4 end style

Let us make a table for -4 ≤ x ≤ 3

x	f(x)
-4	-12
-3	-13
-2	-12
-1	-9
0	-4
1	3
2	12
3	23

if x is integer, then domain of function is D =

begin mathsize 14px style open curly brackets x space colon space x space element of space Z space space a n d space minus 4 space less or equal than space x space less or equal than space 3 space close curly brackets end style

and

range R =

begin mathsize 14px style open curly brackets negative 13 comma space minus 12 comma space minus 9 comma space minus 4 space comma space 3 space comma space 12 space comma space 23 space close curly brackets end style

----------------

if x is real , then domain of function is D =

begin mathsize 14px style open curly brackets x space colon space x space element of R space a n d space minus 4 less or equal than x less or equal than 3 space close curly brackets space end style

Then range is R =

begin mathsize 14px style open curly brackets y space colon space y space element of R space comma space minus 13 space less or equal than y space less or equal than 23 close curly brackets end style

Answered by Thiyagarajan K | 17 Oct, 2023, 09:17: AM

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rang of quadratic expression y=x^2+6x-4 and x belong to (-4,3)

Asked by maheshv9090 | 16 Oct, 2023, 09:30: PM

ANSWERED BY EXPERT

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Q) Find the range of f(x) = x + 1/x Ans) See the image which I have uploaded.. I have just broken the eqn into √x² + 1/√x² +2 -2 ..and have formed the identity (a+b)² and the range is coming (-∞, 2 ] U [ -2, ∞ ) which is wrong.. the correct range is coming from (a-b)² which is (-∞, -2 ] U [ 2, ∞ ). My Doubt- Why (a+b)² is not giving the correct range? Request- Please send the solution using (a+b)². I've attached an image and let me know if I'm wrong somewhere or why the correct solution isn't coming by using (a+b)². Thanks, Samit Future Top 50 ranker in JEE ADVANCE

Asked by samithatty | 01 Dec, 2022, 10:32: PM

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