Q- Let f (x) = 2x² be defined from R to R.
Which of the following is true?
Select all that may apply
a) IF(R)|=IRI<

2 thoughts on “Q- Let f (x) = 2x² be defined from R to R.<br />Which of the following is true?<br />Select all that may apply<br />a) IF(R)|=IRI<”

1. Answer:

   sinθ+cosθ=a

   secθ+cscθ=b

   \sf\underline \red{ To\:Find}

   ToFind

   We have to find the value of b(a²-1)

   \sf\underline \pink{ Solution }

   Solution

   By putting the given values

   \begin{gathered}:\implies\sf\ \ b(a^2-1)\\ \\ \\ :\implies\sf\ \ sec\theta+csc\theta\big\{(sin\theta+cos\theta)^2-1)\big\}\\ \\ \\ \bullet\sf\ sec\theta=\dfrac{1}{cos\theta}\ \ ;\ csc\theta=\dfrac{1}{sin\theta}\\ \\ \\ :\implies\sf\ \dfrac{1}{cos\theta}+\dfrac{1}{sin\theta}\big\{sin^2\theta+cos^2\theta+2sin\theta cos\theta-1\big\}\\ \\ \\ \bullet\sf\ \ sin^2\theta+cos^2\theta=1\\ \\ \\ :\implies\sf\dfrac{sin\theta+cos\theta}{sin\theta\ cos\theta}\big\{\cancel{1}+2sin\theta\ cos\theta \cancel{-1}\big\}\\ \\ \\ :\implies\sf\ \dfrac{sin\theta+cos\theta}{\cancel{sin\theta cos\theta}}\times 2\cancel{sin\theta cos\theta}\\ \\ \\ :\implies\sf\ \ 2(sin\theta+cos\theta)\end{gathered}

   :⟹ b(a

   2

   −1)

   :⟹ secθ+cscθ{(sinθ+cosθ)

   2

   −1)}

   ∙ secθ=

   cosθ

   1

   ; cscθ=

   sinθ

   1

   :⟹

   cosθ

   1

   +

   sinθ

   1

   {sin

   2

   θ+cos

   2

   θ+2sinθcosθ−1}

   ∙ sin

   2

   θ+cos

   2

   θ=1

   :⟹

   sinθ cosθ

   sinθ+cosθ

   {

   1

   +2sinθ cosθ

   −1

   }

   :⟹

   sinθcosθ

   sinθ+cosθ

   ×2

   sinθcosθ

   :⟹ 2(sinθ+cosθ)

   \underline{\bigstar{\blue{\sf\ \ b(a^2-1)= 2(sin\theta+cos\theta)}}}

   ★ b(a

   2

   −1)=2(sinθ+cosθ

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2. Study the figure and answer the following questions.

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?Ø Name the sparsely populated districts with a density of less than 100 per sq. km.

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?Ø Name the sparsely populated districts with a density of less than 100 per sq. km.Ø Name two districts with moderate population densities

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?Ø Name the sparsely populated districts with a density of less than 100 per sq. km.Ø Name two districts with moderate population densitiesØ What is the density of the dark shaded regions?

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?Ø Name the sparsely populated districts with a density of less than 100 per sq. km.Ø Name two districts with moderate population densitiesØ What is the density of the dark shaded regions?Ø Why is the density of population less in Gadchiroli?

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?Ø Name the sparsely populated districts with a density of less than 100 per sq. km.Ø Name two districts with moderate population densitiesØ What is the density of the dark shaded regions?Ø Why is the density of population less in Gadchiroli?Ø Discuss on the effect of physiography, climate, area under forest, industries etc on the density of population.

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?Ø Name the sparsely populated districts with a density of less than 100 per sq. km.Ø Name two districts with moderate population densitiesØ What is the density of the dark shaded regions?Ø Why is the density of population less in Gadchiroli?Ø Discuss on the effect of physiography, climate, area under forest, industries etc on the density of population.class 8 th page no 49. pa ha

   Study the figure and answer the following questions.Ø Which are the most densely populated districts?Ø Name the sparsely populated districts with a density of less than 100 per sq. km.Ø Name two districts with moderate population densitiesØ What is the density of the dark shaded regions?Ø Why is the density of population less in Gadchiroli?Ø Discuss on the effect of physiography, climate, area under forest, industries etc on the density of population.class 8 th page no 49. pa ha if you don’t no then don’t say anything

   Reply