Question

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

Answer 1

Answer:

Correct Question:

If f(x) =x² - 5x +7, Then evaluate f(2)-f(-1)+f(1/3)

Given:

• f(x) = x² - 5x + 7

Find:

• Evaluate f(2) - f(-1) + f(1/3)

Solution:

${ \sf{{Given \: Quadratic \: Equation}{ \red{ \: : f(x) = {x}^{2} - 5x + 7 }}}}$

$: { \implies{ \sf{f(2) = {(2)}^{2} - 5(2) + 7}}} \\ \\ : { \implies{ \sf{f(2) = 4 - 10 + 7}}} \\ \\ : { \implies{ \sf{f(2) = 1}}}$

So, Value of f(2) is 1

$\: : { \implies{ \sf{f( - 1) = {( - 1)}^{2} - 5( - 1) + 7}}} \\ \\ : { \implies{ \sf{f( - 1) = 1 + 5 + 7}}} \\ \\ : { \implies{ \sf{f( - 1) =13 }}}$

So, Value of f(-1) is 13

$\: : { \implies{ \sf{f \bigg( \frac{1}{3} \bigg) = { \bigg( \frac{1}{3} \bigg)}^{2} - 5 \bigg(\frac{1}{3} \bigg) + 7 }}} \\ \\ : { \implies{ \sf{f \bigg( \frac{1}{3} \bigg) = \frac{1}{9} - \frac{5}{3} + 7 }}} \\ \\ : { \implies{ \sf{f \bigg( \frac{1}{3} \bigg) = \frac{49}{9} }}}$

So, Value of f(1/3) is 49/9

$: \implies{ \sf{f(2) - f( - 1) + f \bigg( \frac{1}{3} \bigg)}} \\ \\ : \sf { \implies{1 - 13 + \frac{49}{9} }} \\ \\ : \implies{ \sf{ - 12 + \frac{49}{9} }} \\ \\ : \implies{ \sf{ \frac{ - 59}{9} }}$

${ \therefore \pink{ \sf{{ \sf{f(2) - f( - 1) + f \bigg(\frac{1}{3} \bigg)= \frac{ - 59}{9} }} }}}$