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Question
Let f:R−{−43}→R be a function defined as f(x)=4x3x+4. The inverse of f is the map g:Range f→R−{−43} given by
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Solution
f(x)=4x3x+4Calculating inverse Take f(x)=yy=4x3x+4⇒y(3x+4)=4x∴3xy−4x=−4yx(3y−4)=−4y,x=−4y3y−4∴x=−4y−1(−3y+4)x=4y4−3ySo, inverse of f=(4y−3)6y−4∴g(y)=4y−36y−4
Calculating inverse Take f(x)=y
y=4x3x+4⇒y(3x+4)=4x∴3xy−4x=−4yx(3y−4)=−4y,x=−4y3y−4∴x=−4y−1(−3y+4)x=4y4−3y
So, inverse of f=(4y−3)6y−4
∴g(y)=4y−36y−4
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be
a function defined as
.
The inverse of 
(B) 
(D) 