1.

f-1(1/(x+1)) = 3x+4, then find f(x) = ?

Answer»

f-1\((\frac{1}{x+1})=3x+4\)

\(\therefore\) f-1\(\left(\cfrac{1}{\frac{1-x}x+1}\right)\) = 3\((\frac{1-x}x+4)\)

⇒ f(-1)(x) = 3\((\frac{1-x}x)+4\)---(1)

Let f-1 = y

⇒ f(y) = x

\(\therefore\) From (1), we get

y = \(3(\frac{1-x}x)+4\)

⇒ \(\frac{x(y-4)}3=1-x\) 

⇒ x + x/3(y - 4) = 1

⇒ x (1 + \(\frac{y-4}3\)) = 1

⇒ x \((\frac{3+y-4}3)=1\)

⇒ x (\(\frac{3+y-4}3\)) = 1

⇒ x = 3/y-1

⇒ f(y) = 3/y-1

\(\therefore\) f(x) = 3/x-1


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