Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

The expression $fraction numerator x squared plus 2 x plus 1 over denominator x squared plus 2 x plus 7 end fraction$ lies in the interval ; (x ε R) –

[0, –1]
$(- \infty, 0] \cup [1, \infty)$
[0, 1)
None of these

hint Hint:

In the question, we are required to find the range of the given expression, $fraction numerator x squared plus 2 x plus 1 over denominator x squared plus 2 x plus 7 end fraction$ given that the domain is R.

The correct answer is: [0, 1)

Step by step solution:
Given expression, $fraction numerator x squared plus 2 x plus 1 over denominator x squared plus 2 x plus 7 end fraction$
Let y = $fraction numerator x squared plus 2 x plus 1 over denominator x squared plus 2 x plus 7 end fraction$
$rightwards double arrow y left parenthesis x squared plus 2 x plus 7 right parenthesis$ $equals space x squared plus 2 x plus 1$
$rightwards double arrow x squared y space plus space 2 x y space plus space 7 y$ $equals space x squared plus 2 x plus 1$
$rightwards double arrow x squared left parenthesis y minus 1 right parenthesis$ $plus space 2 x left parenthesis y minus 1 right parenthesis$ $plus left parenthesis 7 y minus 1 right parenthesis$ $equals 0$
Since, $x element of R$
Therefore, $b squared minus 4 a c greater or equal than 0$
$rightwards double arrow left curly bracket 2 left parenthesis y minus 1 right parenthesis right curly bracket squared$ $negative 4 left parenthesis y minus 1 right parenthesis left parenthesis 7 y minus 1 right parenthesis$ $greater or equal than 0$
$rightwards double arrow 4 left parenthesis y squared minus 2 y plus 1 right parenthesis$ $negative 4 left parenthesis 7 y squared minus 8 y plus 1 right parenthesis$ $greater or equal than 0$
$rightwards double arrow y squared minus 2 y plus 1$ $negative 7 y squared plus 8 y minus 1$ $greater or equal than 0$
$rightwards double arrow negative 6 y squared plus 6 y greater or equal than 0$
$rightwards double arrow 6 y squared minus 6 y less or equal than 0$
$rightwards double arrow 6 y left parenthesis y minus 1 right parenthesis less or equal than 0$
$rightwards double arrow y space element of space left square bracket 0 comma 1 right square bracket$
Thus, the expression lies in the interval [0,1]
Hence, option(c) is the correct option.

Related Questions to study

Write the dialogue form of the statement
Matilda said that she would run

Write the dialogue form of the statement
Matilda said that she would run

For every x ε R, the polynomial x⁸ - x⁵ + x² - x + 1 is :

For every x ε R, the polynomial x⁸ - x⁵ + x² - x + 1 is :

If the roots of the quadratic equation x² + 6x + b = 0 are real and distinct and they differ by atmost 4 then the least value of b is –

If the roots of the quadratic equation x² + 6x + b = 0 are real and distinct and they differ by atmost 4 then the least value of b is –

parallel

The number of positive integral solutions of the inequation $fraction numerator x squared left parenthesis 3 x minus 4 right parenthesis cubed left parenthesis x minus 2 right parenthesis to the power of 4 over denominator left parenthesis x minus 5 right parenthesis to the power of 5 left parenthesis 2 x minus 7 right parenthesis to the power of 6 end fraction less or equal than 0$ is

The number of positive integral solutions of the inequation $fraction numerator x squared left parenthesis 3 x minus 4 right parenthesis cubed left parenthesis x minus 2 right parenthesis to the power of 4 over denominator left parenthesis x minus 5 right parenthesis to the power of 5 left parenthesis 2 x minus 7 right parenthesis to the power of 6 end fraction less or equal than 0$ is

Give the comparative form of the adjective Little

Give the comparative form of the adjective Little

Identify run-on Sentences

Identify run-on Sentences

parallel

Identify the meaning of pre when used as a suffix

Identify the meaning of pre when used as a suffix

Identify the tense used in the sentence
He takes but little pride in his work

Identify the tense used in the sentence
He takes but little pride in his work

Identify the tense of the sentence
I shall have spoken.

Identify the tense of the sentence
I shall have spoken.

parallel

Complete the riddle with rhyming word
I am like a deer halo, plucked from a rainbow,
A tight noose brings me to life, With the repeated stab of a _________

Complete the riddle with rhyming word
I am like a deer halo, plucked from a rainbow,
A tight noose brings me to life, With the repeated stab of a _________

Convert the sentence into simple future tense
Lisa makes her parents proud of her achievements

Convert the sentence into simple future tense
Lisa makes her parents proud of her achievements

identify the tense used in the sentence?
Diana had made the breakfast.

identify the tense used in the sentence?
Diana had made the breakfast.

parallel

Identify the predicate in the sentence
She runs 10 miles a day without taking a break

Identify the predicate in the sentence
She runs 10 miles a day without taking a break

The adjoining figure shows the graph of y = ax² + bx + c. Then

The adjoining figure shows the graph of y = ax² + bx + c. Then

If $alpha comma beta comma gamma comma delta$ are roots of $x to the power of 4 minus 100 x cubed plus 2 x squared plus 4 x plus 10 equals 0$ , then $1 over alpha plus 1 over beta plus 1 over gamma plus 1 over delta$ is equal to-

If $alpha comma beta comma gamma comma delta$ are roots of $x to the power of 4 minus 100 x cubed plus 2 x squared plus 4 x plus 10 equals 0$ , then $1 over alpha plus 1 over beta plus 1 over gamma plus 1 over delta$ is equal to-

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.