Question

If f(x) = x2 – 2x and g(x) = 6x + 4, for which value of x does (f + g)(x) = 0?

Answer 1

Answer:  The required value of x is -2.

Step-by-step explanation:  We are given the expressions for two functions f(x) and g(x) as follows :

$f(x)=x^2-2x,~~~~~~g(x)=6x+4.$

We are to find the values of x for which (f + g)(x) = 0.

We know that

for any two functions p(x) and q(x),

$(p+q)(x)=p(x)+q(x).$

We have

$(f+g)(x)=0\\\\\Rightarrow f(x)+g(x)=0\\\\\Rightarrow x^2-2x+6x+4=0\\\\\Rightarrow x^2+4x+4=0\\\\\Rightarrow x^2+\times2x+2^2=0\\\\\Rightarrow (x+2)^2=0\\\\\Rightarrow x+2=0,~~x+2=0\\\\\Rightarrow x=-2.$

Thus, the required value of x is -2.

Answer 2

     G(f(x)) = 2(x^2 -1) + 3

= 2x^2 + 1

subsitute 2

= 9

Hence, the answer is 9