Question

I am really confused ...might anyone know ?

Answer 1

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) ;

`{:\implies \quad \sf f(x)=(x+8)(x-3)}`

We Knows that ;

• 
  `{\boxed{\bf{(a+b)(c+d)=a(c+d)+b(c+d) \:\: \forall \:\:a,b,c,d\in \mathbb{R}}}}`

Using this ;

`{:\implies \quad \sf f(x)=x(x-3)+8(x-3)}`

`{:\implies \quad \sf f(x)=x^(2)-3x+8x-24}`

`{:\implies \quad \sf f(x)=x^(2)+5x-24}`

`{:\implies \quad \bf \therefore \quad \underline{\underline{f(x)=g(x)}}}`

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

Answer 2

Hey there,

formula: (a + b)(c + d) = ac + ad + bc + bd

Determine if the following functions are equivalent.

f(x) = (x + 8)(x - 3)

f(x) = x*x + x*(-3) + 8*x + 8*(-3)

f(x) = x² -3x + 8x - 24

f(x) = x² + 5x - 24

g(x) = x² + 5x - 24

>> f(x) and g(x) are equivalent ✅

Have a nice day ;)