Question
The inverse of f(x)=(5−(x−8)5)13 is
Answer: Option B
:
B
y=f(x)=(5−(x−8)5)13
then y3=5−(x−8)5⇒(x−8)5=5−y3
⇒x=8+(5−y3)15
Let, z=g(x)=8+(5−x3)15
To check, f(g(x))=[5−(x−8)5]13
=(5−[(5−x3)15]5)13=(5−5+x3)13=x
similarly , we can show that g(f(x))=x
Hence, g(x)=8+(5−x3)15 is the inverse of f(x)
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:
B
y=f(x)=(5−(x−8)5)13
then y3=5−(x−8)5⇒(x−8)5=5−y3
⇒x=8+(5−y3)15
Let, z=g(x)=8+(5−x3)15
To check, f(g(x))=[5−(x−8)5]13
=(5−[(5−x3)15]5)13=(5−5+x3)13=x
similarly , we can show that g(f(x))=x
Hence, g(x)=8+(5−x3)15 is the inverse of f(x)
Was this answer helpful ?
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