Prove the following
Question:

If $g(x)=x^{2}+x-1$ and

$(g \circ f)(x)=4 x^{2}-10 x+5$, then $f\left(\frac{5}{4}\right)$ is equal to

  1. $\frac{3}{2}$

  2. $-\frac{1}{2}$

  3. $-\frac{3}{2}$

  4. $\frac{1}{2}$


Correct Option: , 2

Solution:

$g(x)=x^{2}+x-1$

$g(f(x))=4 x^{2}-10 x+5$

$=(2 x-2)^{2}+(2-2 x)-1$

$=(2-2 x)^{2}+(2-2 x)-1$

$\Rightarrow f(x)=2-2 x$

$f\left(\frac{5}{4}\right)=\frac{-1}{2}$

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