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2. The domain of fug is given by: (a) R - (b)R-{0} (c)R-{-2,0)(d) R - {0} 3. The inverse of the function f(x) is a) ( )

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Answer #1

Hey there stay home and stay safe.

How can we solve question 2 without knowing f and g function ?

3)

f(x)=\frac{2-x}{3+x}

Let \ y=f(x)=\frac{2-x}{3+x} \\ y=f(x)\Rightarrow x=f^{-1}(y)\\ Now, y=\frac{2-x}{3+x}\\ \Rightarrow y(3+x)=2-x\\ \Rightarrow 3y+yx=2-x\\ \Rightarrow x+xy=2-3y\\ \Rightarrow x(1+y)=2-3y\\ \Rightarrow x=\frac{2-3y}{y+1}\\ \Rightarrow f^{-1}(y)=\frac{2-3y}{y+1}\\ \Rightarrow f^{-1}(x)=\frac{2-3x}{x+1}\\

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