Question

If f(x)=x^2-5x+7 then evaluate f(2)+f(-2)+f(1/3)=

Answer 1

Answer:

$\dfrac{781}{27}$

Step-by-step explanation:

Note:-

• If f(x) is a function then f(a) is obtained by substituting a in place of xin the given function.
• Here, given f(x) as x^2 -5x +7

f(2):-

• (2)^2 -5(2)+7
• 4-10+7
• 1

f(-2):-

• (-2)^2 -5(-2)+7
• 4+10+7
• 21

f(1/3):-

• (1/3)^2 - 5(1/3) +7
• 1/9 - 5/3 + 7
• $\dfrac{3-5(9)+7(27)}{27}$
• $\dfrac{3-45+189}{27}$
• $\dfrac{147}{27}$

Now , consider f(2) + f(-2) + f(1/3)

• 1 + 21 + $\frac{147}{27}$
• 22 + $\frac{147}{27}$
• $\frac{22(27)+147}{27}$
• $\dfrac{781}{27}$

Therefore,

f(2) + f(-2) + f(1/3) = 781/27

Answer 2

$\bf \red{ \underline{ \underline{solution}}}$

$f(x) = x {}^{2} - 5x + 7$

• Putting the value of x (2)

$f(2) = 2 {}^{2} - 5 \times 2 + 7$

$\implies \: 4 - 10 + 7$

$\implies \: 4 - 3$

$\implies \: 1$

• Putting the value of x (-2)

$f(2) = \: - 2 {}^{2} - 5 \times ( - 2 )+ 7$

$\implies \: 4 + 10 + 7$

$\implies \: 21$

• Putting the value of x (1/3)

$f( \frac{1}{3} ) = ( \frac{1}{3} ) {}^{2} - 5 \times \frac{1}{3} + 7$

$\frac{1}{9 } - \frac{5}{3} + 7$

$\frac{1 - 15 + 63}{9}$

$\implies \frac{ - 14 + 63}{9}$

$\implies \: \frac{49}{9}$

Now,

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

= 1 + 21 + 49/9

=247/9