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Consider f:R+[5,) given by f(x)=9x2+6x5. Show that f is invertible with f1(y)=((y+6)13)

Consider f:R+[5,) given by f(x)=9x2+6x5. Show that f is invertible with f1(y)=((y+6)13)

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Solution:

f:R+[5,) is given as f(x)=9x2+6x5

Let, y be an arbitrary element of, [5,).

Let, y=9x2+6x5

$ \begin{aligned} &\Rightarrow y=(3 x+1)^{2}-1-5=(3 x+1)^{2}-6 \\\\ &\Rightarrow(3 x+1)^{2}=y+6 \\\\ &\Rightarrow 3 x+1=\sqrt{y+6} \quad[\text …

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