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Mark (√) against the correct answer in the following:

Question:

Mark (√) against the correct answer in the following:

Let $f: N \rightarrow X: f(x)=4 x^{2}+12 x+15 .$ Then, $f^{-1}(y)=?$

A. $\frac{1}{2}(\sqrt{\mathrm{y}-4}+3)$

B. $\frac{1}{2}(\sqrt{\mathrm{y}-6}-3)$

C. $\frac{1}{2}(\sqrt{\mathrm{y}-4}+5)$

D. None of these

 

Solution:

$f(x)=4 x^{2}+12 x+15$

$\Rightarrow y=4 x^{2}+12 x+15$

$\Rightarrow y=(2 x+3)^{2}+6$

$\Rightarrow \sqrt{(} y-6)=2 x+3$

$\Rightarrow \frac{1}{2}(\sqrt{y-6}-3)=x$

$f^{-1}(y)=\frac{1}{2}(\sqrt{y-6}-3)$

 

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