Question

if f(x) = x² - 5x + 1 then evaliate f(2) - f(-1) + f(⅓)​

Answer 1

$\large\sf\underline{Given\::}$

Polynomial :

• $\sf\:f(x)~=~x^{2}-5x+1$

‎

$\large\sf\underline{To\::}$

• Calculate the value of [ f(2) - f(-1) + f(⅓) ]

‎

$\large\sf\underline{Concept\::}$

Here we are given a polynomial f(x) = x² - 5x + 1 and we are asked to evaluate the value of f(2) - f(-1) + f(⅓) .

We would solve this question in 4 steps. At first, we would calculate the value of f(2) , by substituting 2 in place of x in the given polynomial, similarly we would calculate the value of f(-1) , f(⅓) . Then finally we would substitute the value of f(2) , f(-1) and f(⅓) in f(2) - f(-1) + f(⅓) . Doing so we will get our final answer.

Let's do it :D !!

‎

$\large\sf\underline{Solution\::}$

$\small{\mathfrak{1^{st}~step~:~Calculating~the~value~of~f(2)}}$

$\sf\:Given~polynomial~f(x) ~=~x^{2}-5x+1$

• Substituting the value of x as 2

$\sf\dashrightarrow\:f(2) ~=~2^{2}-5 \times 2+1$

$\sf\dashrightarrow\:f(2) ~=~4-10+1$

$\sf\dashrightarrow\:f(2) ~=~-6+1$

$\small{\underline{\boxed{\mathrm{\dashrightarrow~f(2)~=~(-5)}}}}$

_____________

$\small{\mathfrak{2^{nd}~step~:~Calculating~the~value~of~f(-1)}}$

$\sf\:Given~polynomial~f(x) ~=~x^{2}-5x+1$

• Substituting the value of x as ( - 1 )

$\sf\dashrightarrow\:f(-1) ~=~(-1)^{2}-5 \times (-1)+1$

$\sf\dashrightarrow\:f(-1) ~=~1-(-5)+1$

$\sf\dashrightarrow\:f(-1) ~=~1+5+1$

$\sf\dashrightarrow\:f(-1) ~=~6+1$

$\small{\underline{\boxed{\mathrm{\dashrightarrow\:f(-1)\:=\:7}}}}$

_____________

$\small{\mathfrak{3^{rd}~step~:~Calculating~the~value~of~f(⅓)}}$

$\sf\:Given~polynomial~f(x) ~=~x^{2}-5x+1$

• Substituting the value of x as ( ⅓ )

$\sf\dashrightarrow\:f(⅓) ~=~(⅓)^{2}-5 \times (⅓)+1$

$\sf\dashrightarrow\:f(⅓) ~=~\frac{1}{9}-\frac{5}{3}+1$

• LCM of 9 and 3 = 9

$\sf\dashrightarrow\:f(⅓) ~=~\frac{1-15+9}{9}$

$\sf\dashrightarrow\:f(⅓) ~=~\frac{-14+9}{9}$

$\small{\underline{\boxed{\mathrm{\dashrightarrow\: f(⅓) ~=~\frac{-5}{9}}}}}$

_____________

$\small{\mathfrak{Final~step~:~Calculating~the~value~of~f(2)-f(-1)+f(⅓)}}$

$\sf\:f(2) - f(-1) + f(⅓)$

• Substituting the values we got for f(2) , f(-1) and f(⅓)

$\sf\dashrightarrow\: (-5)- 7 + \frac{-5}{9}$

$\sf\dashrightarrow\: -5- 7 + \frac{-5}{9}$

$\sf\dashrightarrow\:\frac{[9 \times (-5)]-(9 \times 7)+[1 \times (-5)]}{9}$

$\sf\dashrightarrow\:\frac{[-45]-(63)+[-5]}{9}$

$\sf\dashrightarrow\:\frac{-45-63-5}{9}$

$\sf\dashrightarrow\:\frac{-108-5}{9}$

$\small{\underline{\boxed{\mathrm\red{\dashrightarrow\:f(2) - f(-1) + f(⅓) ~=~\frac{-113}{9}}}}}$ ★

===================

Note :- Scroll left to right to view the full solution !~

Answer 2

$[tex]\large\sf\underline{Given\::}$

Polynomial :

$\sf\:f(x)~=~x^{2}-5x+1$

‎

$\large\sf\underline{To\::}$

Calculate the value of [ f(2) - f(-1) + f(⅓) ]

‎

$\large\sf\underline{Concept\::}$

Here we are given a polynomial f(x) = x² - 5x + 1 and we are asked to evaluate the value of f(2) - f(-1) + f(⅓) .

We would solve this question in 4 steps. At first, we would calculate the value of f(2) , by substituting 2 in place of x in the given polynomial, similarly we would calculate the value of f(-1) , f(⅓) . Then finally we would substitute the value of f(2) , f(-1) and f(⅓) in f(2) - f(-1) + f(⅓) . Doing so we will get our final answer.

Let's do it :D !!

‎

$\large\sf\underline{Solution\::}$

$\small{\mathfrak{1^{st}~step~:~Calculating~the~value~of~f(2)}}$

$\sf\:Given~polynomial~f(x) ~=~x^{2}-5x+1$

Substituting the value of x as 2

$\sf\dashrightarrow\:f(2) ~=~2^{2}-5 \times 2+1$

$\sf\dashrightarrow\:f(2) ~=~4-10+1$

$\sf\dashrightarrow\:f(2) ~=~-6+1$

$\small{\underline{\boxed{\mathrm{\dashrightarrow~f(2)~=~(-5)}}}}$

_____________

$\small{\mathfrak{2^{nd}~step~:~Calculating~the~value~of~f(-1)}}$

$\sf\:Given~polynomial~f(x) ~=~x^{2}-5x+1$

Substituting the value of x as ( - 1 )

$\sf\dashrightarrow\:f(-1) ~=~(-1)^{2}-5 \times (-1)+1$

$\sf\dashrightarrow\:f(-1) ~=~1-(-5)+1$

$\sf\dashrightarrow\:f(-1) ~=~1+5+1$

$\sf\dashrightarrow\:f(-1) ~=~6+1$

$\small{\underline{\boxed{\mathrm{\dashrightarrow\:f(-1)\:=\:7}}}}$

_____________

$\small{\mathfrak{3^{rd}~step~:~Calculating~the~value~of~f(⅓)}}$

$\sf\:Given~polynomial~f(x) ~=~x^{2}-5x+1$

Substituting the value of x as ( ⅓ )

$\sf\dashrightarrow\:f(⅓) ~=~(⅓)^{2}-5 \times (⅓)+1$

$\sf\dashrightarrow\:f(⅓) ~=~\frac{1}{9}-\frac{5}{3}+1$

LCM of 9 and 3 = 9

$\sf\dashrightarrow\:f(⅓) ~=~\frac{1-15+9}{9}$

$\sf\dashrightarrow\:f(⅓) ~=~\frac{-14+9}{9}$

$\small{\underline{\boxed{\mathrm{\dashrightarrow\: f(⅓) ~=~\frac{-5}{9}}}}}$

_____________

$\small{\mathfrak{Final~step~:~Calculating~the~value~of~f(2)-f(-1)+f(⅓)}}$

$\sf\:f(2) - f(-1) + f(⅓)$

Substituting the values we got for f(2) , f(-1) and f(⅓)

$\sf\dashrightarrow\: (-5)- 7 + \frac{-5}{9}$

$\sf\dashrightarrow\: -5- 7 + \frac{-5}{9}$

$\sf\dashrightarrow\:\frac{[9 \times (-5)]-(9 \times 7)+[1 \times (-5)]}{9}$

$\sf\dashrightarrow\:\frac{[-45]-(63)+[-5]}{9}$

$\sf\dashrightarrow\:\frac{-45-63-5}{9}$

$\sf\dashrightarrow\:\frac{-108-5}{9}$

$\small{\underline{\boxed{\mathrm\red{\dashrightarrow\:f(2) - f(-1) + f(⅓) ~=~\frac{-113}{9}}}}}$ ★

===================

Note :- Scroll left to right to view the full solution !~[/tex]