Answer
425.1k+ views
Hint: We have given a function $ f(x)=\dfrac{3x+5}{2x-3} $ and we have to find the value of $ f\left( 15 \right)+f\left( -10 \right)= $ we put the value of $ x=15 $ and $ x=-10 $ in the given function one by one and calculate the value of $ f\left( 15 \right) $ and $ f\left( -10 \right) $ . Then, add both to obtain a desired result.
Complete step-by-step answer:
We have given that $ f(x)=\dfrac{3x+5}{2x-3} $
We have to find the value of $ f\left( 15 \right)+f\left( -10 \right) $ .
Now, first we calculate the value of $ f(15) $ , for this we put the value $ x=15 $ in the given equation.
When we put value, we get
$ \begin{align}
& f(x)=\dfrac{3x+5}{2x-3} \\
& f(15)=\dfrac{3\times 15+5}{2\times 15-3} \\
\end{align} $
Now, simplify the equation to solve further
\[\begin{align}
& f(15)=\dfrac{45+5}{30-3} \\
& f(15)=\dfrac{50}{27}.......(i) \\
\end{align}\]
Similarly, we calculate the value of $ f(-10) $ .
When we put the value $ x=-10 $ in the given equation, we get
$ \begin{align}
& f(x)=\dfrac{3x+5}{2x-3} \\
& f(-10)=\dfrac{3\times \left( -10 \right)+5}{2\times \left( -10 \right)-3} \\
& f(-10)=\dfrac{-30+5}{-20-3} \\
& f(-10)=\dfrac{-25}{-23} \\
& f(-10)=\dfrac{25}{23}.................(ii) \\
\end{align} $
Now, to find the value of $ f\left( 15 \right)+f\left( -10 \right) $ , substitute the value from equation (i) and equation (ii)
$ f\left( 15 \right)+f\left( -10 \right)=\dfrac{50}{27}+\dfrac{25}{23} $
Now, take LCM to solve further, as $ 27 $ and $ 23 $ don’t have common factor, we directly cross multiply to solve
$ \begin{align}
& f\left( 15 \right)+f\left( -10 \right)=\dfrac{50\times 23+27\times 25}{27\times 23} \\
& f\left( 15 \right)+f\left( -10 \right)=\dfrac{1150+675}{621} \\
& f\left( 15 \right)+f\left( -10 \right)=\dfrac{1825}{621} \\
\end{align} $
Hence, the value of $ f\left( 15 \right)+f\left( -10 \right)=\dfrac{1825}{621} $.
So, the correct answer is “Option C”.
Note: One may relate this question with the differentiation as the given equation is of the form $ f(x)=\dfrac{3x+5}{2x-3} $. But we have to find the value of $ f\left( 15 \right)+f\left( -10 \right) $, which are not derivatives so it is not a question of differentiation. If it is asked to find the value of $ f'\left( 15 \right)+f'\left( -10 \right) $ instead of $ f\left( 15 \right)+f\left( -10 \right) $, then we first differentiate the given equation and find the values.
Complete step-by-step answer:
We have given that $ f(x)=\dfrac{3x+5}{2x-3} $
We have to find the value of $ f\left( 15 \right)+f\left( -10 \right) $ .
Now, first we calculate the value of $ f(15) $ , for this we put the value $ x=15 $ in the given equation.
When we put value, we get
$ \begin{align}
& f(x)=\dfrac{3x+5}{2x-3} \\
& f(15)=\dfrac{3\times 15+5}{2\times 15-3} \\
\end{align} $
Now, simplify the equation to solve further
\[\begin{align}
& f(15)=\dfrac{45+5}{30-3} \\
& f(15)=\dfrac{50}{27}.......(i) \\
\end{align}\]
Similarly, we calculate the value of $ f(-10) $ .
When we put the value $ x=-10 $ in the given equation, we get
$ \begin{align}
& f(x)=\dfrac{3x+5}{2x-3} \\
& f(-10)=\dfrac{3\times \left( -10 \right)+5}{2\times \left( -10 \right)-3} \\
& f(-10)=\dfrac{-30+5}{-20-3} \\
& f(-10)=\dfrac{-25}{-23} \\
& f(-10)=\dfrac{25}{23}.................(ii) \\
\end{align} $
Now, to find the value of $ f\left( 15 \right)+f\left( -10 \right) $ , substitute the value from equation (i) and equation (ii)
$ f\left( 15 \right)+f\left( -10 \right)=\dfrac{50}{27}+\dfrac{25}{23} $
Now, take LCM to solve further, as $ 27 $ and $ 23 $ don’t have common factor, we directly cross multiply to solve
$ \begin{align}
& f\left( 15 \right)+f\left( -10 \right)=\dfrac{50\times 23+27\times 25}{27\times 23} \\
& f\left( 15 \right)+f\left( -10 \right)=\dfrac{1150+675}{621} \\
& f\left( 15 \right)+f\left( -10 \right)=\dfrac{1825}{621} \\
\end{align} $
Hence, the value of $ f\left( 15 \right)+f\left( -10 \right)=\dfrac{1825}{621} $.
So, the correct answer is “Option C”.
Note: One may relate this question with the differentiation as the given equation is of the form $ f(x)=\dfrac{3x+5}{2x-3} $. But we have to find the value of $ f\left( 15 \right)+f\left( -10 \right) $, which are not derivatives so it is not a question of differentiation. If it is asked to find the value of $ f'\left( 15 \right)+f'\left( -10 \right) $ instead of $ f\left( 15 \right)+f\left( -10 \right) $, then we first differentiate the given equation and find the values.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)