Functions: If g(x)=x^2+x-1 and (gcirc f)(x)=4x^2-10x+5 , then f (frac54 ) is… | JEE Main 2020 | Yukti Vault

Yukti Vault

JEE Main 2020 (Online) 7th January Morning ShiftQuestion 1

If $g(x)=x^{2}+x-1$ and $(g\circ f)(x)=4x^{2}-10x+5$, then $f\left(\frac54\right)$ is equal to

Functions

$\frac32$$-\frac12$✓ Correct answer$\frac12$$-\frac32$

Solution

At $x=\frac54$: $g(f)=4\cdot\frac{25}{16}-\frac{25}{2}+5=-\frac54$. So $f^2+f-1=-\frac54$, $(f+\frac12)^2=0$, $f=-\frac12$.

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