COMEDK2014MathematicsFunctions

If f(x)= 2 x-3 3 x+4 , then f⁻¹ ( -4 3 )=

Options

AZero
B3 4
C- 2 3
DNone of these

Correct answer

D. None of these

Step-by-step solution

f(x)= 2 x-3 3 x+4 Let f(x)=y= 2 x-3 3 x+4 On cross multiplication, we get aligned &3 x y+4 y=2 x-3 & x(3 y-2)=-3-4 y & x= -3-4 y 3 y-2 x=f⁻¹(y)= -3-4 y 3 y-2 aligned Put y=- 4 3 , we get aligned f⁻¹ (- 4 3 ) &= -3-4 (- 4 3 ) 3 (- 4 3 )-2 &= -3+ 16 3 -4-2 = 7 3 (-6) =- 7 18 aligned

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