Question
If the function f:[1,∞)→[1,∞) is defined by f(x)=2x(x−1), then f−1(x) is
Answer: Option B
:
B
f(x)=y⇒2x(x−1)=y⇒x(x−1)log22=log2y
⇒x(x−1)=log2y⇒x2−x−log2y=0
⇒x=1±√1+4log2y2
∴x=1+√1+4log2y2
∴f−1(x)=12(1+√1+4log2x)
∴ The correct answer is (b).
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:
B
f(x)=y⇒2x(x−1)=y⇒x(x−1)log22=log2y
⇒x(x−1)=log2y⇒x2−x−log2y=0
⇒x=1±√1+4log2y2
∴x=1+√1+4log2y2
∴f−1(x)=12(1+√1+4log2x)
∴ The correct answer is (b).
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