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Q.

If (f(x))2×f1−x1+x=64x; ∀x∈Df, thenf (x) is equal toThe domain of f (x) isThe value of f (9/7) is

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a

4x2/31+x1−x1/3

b

x1/31−x1+x1/3

c

x1/31−x1+x1/3

d

x1+x1−x1/3

e

[0, ∞)

f

R−{1}

g

(−∞, ∞)

h

none of these

i

8(7/9)2/3

j

4(9/7)1/3

k

−8(9/7)2/3

l

none of these

answer is , , .

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Detailed Solution

(f(x))2f1−x1+x=64x          (1) Putting 1−x1+x=y or x=1−y1+y, we getf1−y1+y2⋅f(y)=641−y1+yor   f(x)⋅f1−x1+x2=641−x1+x                 (2)Squaring (1) and dividing by (2), f(x)4f1−x1+x2f(x)f1−x1+x2=(64x)2641−x1+xor  {f(x)}3=64x21+x1−xor  f(x)=4x2/31+x1−x1/3 (f(x))2f1−x1+x=64x          (1) Putting 1−x1+x=y or x=1−y1+y, we getf1−y1+y2⋅f(y)=641−y1+yor   f(x)⋅f1−x1+x2=641−x1+x                 (2)Squaring (1) and dividing by (2), f(x)4f1−x1+x2f(x)f1−x1+x2=(64x)2641−x1+xor  {f(x)}3=64x21+x1−xor  f(x)=4x2/31+x1−x1/3 (f(x))2f1−x1+x=64x          (1) Putting 1−x1+x=y or x=1−y1+y, we getf1−y1+y2⋅f(y)=641−y1+yor   f(x)⋅f1−x1+x2=641−x1+x                 (2)Squaring (1) and dividing by (2), f(x)4f1−x1+x2f(x)f1−x1+x2=(64x)2641−x1+xor  {f(x)}3=64x21+x1−xor  f(x)=4x2/31+x1−x1/3or  x=f(9/7)=−4(9/7)2/3(2)
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