Question

12. If f(x) = x² – 5x + 7, evaluate f(2) – f(-1) + f(1/3)​

Answer 1

Answer:

∴ f(2)-f(-1)+f(1/3) = -59/9

Step-by-step explanation:

Given,

f(x) = x²-5x+7

f(2)-f(-1)+f(1/3) = ?

Now,

f(2) = 2²-5×2+7 = 4-10+7 = 1

Again,

f(-1) = (-1)²-5×(-1)+7 = 1+5+7 = 13

Again,

f(1/3) = (1/3)²-5×1/3+7 = 1/9-5/3+7 = (1-15+63)/9 = 49/9

Therefore,

f(2)-f(-1)+f(1/3) = 1-13+49/9 = (9-117+49)/9 = -59/9

Answer 2

$\huge\underline\mathfrak{Solution:}$

Given,

$f(x) = {x}^{2} - 5x + 7 \\ f(2) = {(2)}^{2} - (5)2 + 7 \\ = > f(2) = 4 - 10 + 7 \\ = > f(2) = 1 \\ f( - 1) = {( - 1)}^{2} - 5( - 1) + 7 \\ = > f( - 1) = 1 + 5 + 7 = 13 \\ \\ f \frac{(1)}{(3) } = \frac{(1)}{(3)} {}^{2} - 5 \frac{(1)}{(3)} + 7 \\ = > f \frac{(1)}{(3)} = \frac{1}{9} - \frac{5}{3} + 7 \\ = > f \frac{(1)}{(3)} = \frac{1 - 15 + 63}{9 } \\ = > f \frac{(1)}{(3)} = \frac{64 - 15}{9} \\ = > f \frac{(1)}{(3)} = \frac{49}{9} \\ \\ now \: f(2) - f( - 1) + f \frac{1}{3} \\ = 1 - 13 + \frac{49}{9} \\ = - 12 + \frac{49}{7} \\ = \frac{ - 84 + 49}{7} \\ = \frac{ - 35}{7} \\ = - 5$

$\huge{\boxed{\boxed{Ans.-5}}}$