We are given with two functions f(x) & g(x) respectively , with 3 options and have to choose correct option
Now , here g(x) is already in simplified form , so let's simplify f(x) ;
[tex]{:\implies \quad \sf f(x)=(x+8)(x-3)}[/tex]
We Knows that ;
- [tex]{\boxed{\bf{(a+b)(c+d)=a(c+d)+b(c+d) \:\: \forall \:\:a,b,c,d\in \mathbb{R}}}}[/tex]
Using this ;
[tex]{:\implies \quad \sf f(x)=x(x-3)+8(x-3)}[/tex]
[tex]{:\implies \quad \sf f(x)=x^{2}-3x+8x-24}[/tex]
[tex]{:\implies \quad \sf f(x)=x^{2}+5x-24}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{f(x)=g(x)}}}[/tex]
As f(x) = g(x) . So f(x) & g(x) are equivalent.
Hence , Option 3) f(x) and g(x) are equivalent is correct :D
