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Need help answering these to QuestionsCan’t seem to understand, really struggling

Need help answering these to QuestionsCan’t seem to understand, really struggling-example-1
User AdamL
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The functions are given as,


\begin{gathered} f(x)=3x+2 \\ g(x)=x^2+x-6 \\ h(x)=-2x\cdot f(x)-g(x) \end{gathered}

Substitute the values of f(x) and g(x) in h(x), and simplify,


\begin{gathered} h(x)=-2x\cdot(3x+2)-(x^2+x-6) \\ h(x)=-2x\cdot(3x)-2x\cdot(2)-x^2-x+6 \\ h(x)=-6x^2-4x-x^2-x+6 \\ h(x)=-7x^2-5x+6 \end{gathered}

Thus, option C is the correct choice as it represents the correct expression of the function h(x).

Consider the given function g(x) as,


g(x)=-\sqrt[]{x+3}+2

Since the function f(x) is not given here, we will use the same function from the above part of the problem,


f(x)=3x+2

According to the given condition,


f(x)=g(x)

Substitute the values,


\begin{gathered} 3x+2=-\sqrt[]{x+3}+2 \\ 3x=-\sqrt[]{x+3} \end{gathered}

Consider this as the parent equation.

Square both sides,


\begin{gathered} 9x^2=x+3 \\ 9x^2-x-3=0 \end{gathered}

Apply the quadratic formula,


\begin{gathered} x=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(9)(-3)}}{2(9)} \\ x=\frac{1\pm\sqrt[]{1+108}}{18} \\ x=\frac{1+\sqrt[]{109}}{18},\frac{1-\sqrt[]{109}}{18} \end{gathered}

Consider that the square root term cannot contain any negative number inside. So the following solution is not feasible,


x=\frac{1-\sqrt[]{109}}{18}

So, the only feasible solution of the parent equation is,


x=\frac{1+\sqrt[]{109}}{18}

Thus, there is only one value of 'x' that satisfies the condition.

Therefore, option B is the correct choice.

User Oink
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