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in Sets, Relations and Functions by (27.7k points)
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Mark (√) against the correct answer in the following:

Let \(f:R-{\frac{-4}{3}}→-{\frac{4}{3}}:f(x)=\frac{4x}{(3x+4)}.\) Then f-1(y) = ?

A. \(\frac{4y}{(4-3y)}\)

B. \(\frac{4y}{(4y+3)}\)

C. \(\frac{4y}{(3y-4)}\)

D. None of these

1 Answer

+1 vote
by (25.7k points)
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Best answer

Correct Answer is (A) \(\frac{4y}{(4-3y)}\)

f(x) =\(\frac{4x}{(3x+4)}\)

⇒y =\(\frac{4x}{(3x+4)}\)

x ⟺ y

⇒x =\(\frac{4y}{(3y+4)}\)

⇒3yx + 4x = 4y

⇒y(3x - 4) = - 4x

⇒y = \(\frac{4x}{(4-3x)}\)

x ⟺ y

⇒x = \(\frac{4y}{(4-3y)}\)

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