A) \[-\frac{1}{2}\]
B) \[\frac{3}{2}\]
C) \[\frac{1}{2}\]
D) \[-\frac{3}{2}\]
Correct Answer: A
Solution :
[a] \[g\left( f\left( \frac{5}{4} \right) \right)=4{{\left( \frac{5}{4} \right)}^{2}}-10\left( \frac{5}{4} \right)+5=\frac{-5}{4}\] Now, \[g\left( f\left( \frac{5}{4} \right) \right)={{f}^{2}}\left( \frac{5}{4} \right)+f\left( \frac{5}{4} \right)-1\] Let \[f\left( \frac{5}{4} \right)=t\] \[\Rightarrow {{t}^{2}}+t-1=\frac{-5}{4}\] \[{{t}^{2}}+t+\frac{1}{4}=0\] \[\therefore {{\left( t+\frac{1}{2} \right)}^{2}}=0\] i.e., \[f\left( \frac{5}{4} \right)=\frac{-1}{2}\]
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