CAN ANYONE SOLVE THIS STEP BY STEP

ALIAHMAD

ALIAHMAD

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[imath]\sqrt{ \log_{ 0.4 }({ x- { x }^{ 2 } }) \phantom{\tiny{!}}}[/imath]
 
ALIAHMAD said:
[imath]\sqrt{ \log_{ 0.4 }({ x- { x }^{ 2 } }) \phantom{\tiny{!}}}[/imath]
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What is the question? What did you want to find?

Please post the complete problem - along with your attempt to solve it.
 
The honest answer to your question is no, nobody can solve this.
 
Subhotosh Khan said:
What is the question? What did you want to find?

Please post the complete problem - along with your attempt to solve it.
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SIR PLEASE FIND THE DOMAIN OF THE ABOVE FUNCTION OR IN SIMPLE WORDS WHAT ARE THE VALUES OF X

Steven G said:
The honest answer to your question is no, nobody can solve this.
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I DIDN'T QUITE UNDERSTAND IT.
"SIR PLEASE FIND THE DOMAIN OF THE ABOVE FUNCTION OR IN SIMPLE WORDS WHAT ARE THE VALUES OF X"
PLEASE ADD THIS TO THE ABOVE QUESTION AND THEN PLEASE SOLVE IT
I REALLY NEED THE ANSWER
 
ALIAHMAD said:
I REALLY NEED THE ANSWER
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Do you have any experience finding domains? For example, are you able to find the domain of this simpler version?

\(\displaystyle \sqrt{x - x^2}\)

Also, are you familiar with the change-of-base formula for logarithms?

[imath]\;[/imath]
 
mmm4444bot said:
Please read the forum's guidelines. Here's a link to a summary.

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com

Do you have any experience finding domains? For example, are you able to find the domain of this simpler version?

\(\displaystyle \sqrt{x - x^2}\)

[imath]\;[/imath]
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YES, I CAN SOVE IT THE DOMAIN OF THE FUNCTION [math]\sqrt{ x- { x }^{ 2 } \phantom{\tiny{!}}}[/math] IS x belongs to [0,1]

mmm4444bot said:
Please read the forum's guidelines. Here's a link to a summary.

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to help...
www.freemathhelp.com

Do you have any experience finding domains? For example, are you able to find the domain of this simpler version?

\(\displaystyle \sqrt{x - x^2}\)

Also, are you familiar with the change-of-base formula for logarithms?

[imath]\;[/imath]
Click to expand...
YEAH LIKE IF THE BASE OF LOG IS 0<x<1 THEN WHILE REMOVING LOG THE SIGN OF INEQUALITY CHANGES
BUT IF THE BASE x>1 THEN SIGN OF INEQUALITY DOESN'T CHNAGE
 
I would set the log function part greater than or equal to 0 and find the domain . Because you can only take square root of positive values.
 
Qwertyuiop[] said:
I would set the log function part greater than or equal to 0 and find the domain . Because you can only take square root of positive values.
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I DON'T THINK THIS IS HOW LOG FUNCTIONS WORK WHEN GIVEN A CONSTANT BASE.
 
You have two constraints to consider.
1) You can't take the square root of a negative number (equivalent to what you take the square root of must be >=0)
2) You can only compute the log of a positive value.

log0.4(x-x2)> 0
x-x2>0
 
Steven G said:
You have two constraints to consider.
1) You can't take the square root of a negative number (equivalent to what you take the square root of must be >=0)
2) You can only compute the log of a positive value.

log0.4(x-x2)> 0
x-x2>0
Click to expand...
In this case I got the answer as x belongs to [0,1]
 
But the square root must also be >=0
Therefore x(x-1)>=-1
Which is x²-x+1>=0
Gives no answer as d=b²-4ac gives me negative value
 
You have [math]f(x) = g(h(i(x))), \text { where } i(x) = x - x^2,\\ h(x) = log_{0.4}(x), \text { and } g(x) = \sqrt{x}.[/math]
The way to do these problems is to start from the inside out.

What is the domain of i(x)? All real numbers.

What is the domain of h(x), a log function? What is the domain of any log function? [imath](0, \infty)[/imath].

So x values for which

[math]i(x) > 0 \implies x - x^2 > 0 \implies x > x^2.\\ x < 0 \implies 0 < x^2 \implies x < x^2 \implies x \not < 0.\\ x = 0 \implies x = x^2 \implies x \ne 0.\\ \therefore \ 0 < x.\\ x \ge 1 \implies x > 0 \implies x * x \ge x * 1 \implies x^2 \ge x \implies x < 1.\\ \text {In short, } 0 < x < 1.[/math]
Thus, the domain of f(x) cannot be LARGER THAN (0, 1). But it could be smaller. You have not completed the task.

Given x in (0, 1), what is the range of h(x)?

Is that larger than the domain of g(x).

If so, what next?
 
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