Question

Consider functions f and g.1 + 12f(1) = 12 + 4. – 12for * # 2 and 7 -64.2 – 16. + 1641 +48for a # -12 Which expression is equal to f(x) · g(t)?OA.41 - 81 + 61OB.SIKIAOC.21 + 6I + 2D.6

Answer 1

Given the following functions below,

`\begin{gathered} f(x)=(x+12)/(x^2+4x-12)\text{ and} \\ g(x)=(4x^2-16x+16)/(4x+48) \end{gathered}`

Factorising the denominators of both functions,

Factorising the denominator of f(x),

`\begin{gathered} f(x)=(x+12)/(x^2+4x-12)=(x+12)/(x^2+6x-2x-12)=(x+12)/(x(x+6)-2(x+6))=(x+12)/((x-2)(x+6)) \\ f(x)=(x+12)/((x-2)(x+6)) \end{gathered}`

Factorising the denominator of g(x),

`\begin{gathered} g(x)=(4x^2-16x+16)/(4x+48)=(4(x^2-4x+4))/(4(x+12)) \\ \text{Cancel out 4 from both numerator and denominator} \\ g(x)=(x^2-4x+4)/(x+12)=(x^2-2x-2x+4)/(x+12)=(x(x-2)-2(x-2))/(x+12)=((x-2)^2)/(x+12) \\ g(x)=((x-2)^2)/(x+12) \end{gathered}`

Multiplying both functions,