JEE 2023 — Mathematics PYQ

Hume pata hai ki:

Yahan $g(x)$ ki value put karne par:

2. Variable Substitution

Hume $f(0)$ nikalna hai, iska matlab bracket ke andar ki term $(\sqrt{x}+1)$ zero honi chahiye.

Maana $\sqrt{x}+1=t$

Jab hume $f(0)$ chahiye, toh hum $t=0$ rakhenge:

3. Value Put Karna

Ab upar wali equation $f(\sqrt{x}+1)=x+3-\sqrt{x}$ mein $\sqrt{x}=-1$ ki value rakhte hain:

Final Answer

Sahi option (1) 5 hai.

Alternate Method (General Function nikal kar):

Agar aap $f(t)$ nikalna chahte hain:

$\sqrt{x}=t-1⟹x=(t-1{)}^2$

Ab $t=0$ rakhne par: $f(0)=5$.