Question

Whiuch statement is true about the equation f(x)= g(x) given f(x) = 2x+ 3 and g(x) = x^2??a.it has two solutions -1 and 3b. it has two solutions -1.5 and 0c. it has four solutions at -1, 1, 3 and 9d. it has four solutions at -1.5, -1, 0 ,and 3

Answer 1

Determine the equation of x for f(x)=g(x).

`\begin{gathered} f(x)=g(x) \\ 2x+3=x^2 \\ x^2-2x-3=0 \end{gathered}`

Simplify the equation for x.

`\begin{gathered} x^2-3x+x-3=0 \\ x(x-3)+1(x-3)=0 \\ (x+1)(x-3)=0 \end{gathered}`

So possible values of x are,

`\begin{gathered} x+1=0 \\ x=-1 \end{gathered}`

and

`\begin{gathered} x-3=0 \\ x=3 \end{gathered}`

So equation has two solutions and equal to -1 and 3.