Question

Let f : R – {-4/3} → R be a function given by f(x) = 4x/(3x+4). Show that f is invertible with −1 (x) = 4x/(4-3x)
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Answer 1

Given :   f : R – {-4/3} → R be a function given by f(x) = 4x/(3x+4)

To Find : Show that f is invertible with f⁻¹ (x) = 4x/(4-3x)

Solution:

f(x)  = 4x/(3x + 4)

y = 4x/(3x + 4)

=> 3xy + 4y  = 4x

=> 4y  = 4x - 3xy

=> 4y = x( 4 - 3y)

=> x = 4y/(4 - 3y)

f⁻¹(x)  = 4x/(4 - 3x)

Learn More:

क्या निम्नलिखित वास्तविक चर के वास्तविक-मानित फलन का प्रतिलोम फलन प्राप्त होग

कारण  f(x)=|x|

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