Question

Answer the question in attachment​

Answer 1

$\huge{\red{\fbox{\green{\fbox{\green{\underline{\purple{Answer}}}}}}}}$

$\large{\green{\fbox{\fbox{\pink{\underline{\blue{\star\;Note}}}}}}}$

n! = n(n-1)(n-2).......1

$\large{\orange{\fbox{\fbox{\blue{\underline{\green{\star\;Solution}}}}}}}$

$\large{\orange{\fbox{\blue{\fbox{\green{\fbox{\pink{To\;find\;value\;of\;g(10)}}}}}}}}$

Given,

• g(r) = 1/r , r € [1,9]

• g(r) - 1/r = 0

• rg(r)-1 = 0

Given r can be equal to 1 , 2 , ......9

• rg(r)-1 = k (r-1)(r-2)....(r-9) -------(1)

Put r = 0

• -1 = k (-1)(-2)(-3)....(-9)

• k = 1/9!

Now put r = 10 in equation (1)

• 10 g(10)-1 = 1/9! (10-1)(10-2).....(10-9)

• 10 g(10)-1 = 1/9! × 9!

• 10 g(10)-1 = 1

• g(10) = 1/5

$\large{\orange{\fbox{\blue{\fbox{\green{\fbox{\pink{To\;find\;value\;of\;f(-1)\;put\;x\;=\;-1\;in\;f(x)}}}}}}}}$

• f(-1) = (-1-1)(-1/2 -1)(-1/3 -1).....(-1/9 -1)

• f(-1) = (-2)(-3/2)(-4/3)......(-10/9)

• f(-1) = 10

$\large{\orange{\fbox{\blue{\fbox{\green{\fbox{\purple{Required\;value}}}}}}}}$

• f(-1) ÷ g(10) = 10 ÷ 1/5

• f(-1) ÷ g(10) = 50