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Functions

SAT Functions

\[f(x)=x^{2}-25\] \[g(x)=\sqrt{25-x^{2}}\]

The functions \(f\) and \(g\) are defined above. Which of the following is the domain of \(f(g(x))\)?

(A) \(\ \ x < -5\)
(B) \(\ \ x \leq 5\)
(C) \(\ \ -5 \leq x \leq 5\)
(D) \(\ \ x > 25\)
(E) \(\ \ \)All real numbers

\[\begin{array}{l c l} f(x) &=& x^{2}-3\\ g(x) &=& x+7\\ \end{array}\]

Which of the following equals \(f(11) - g(6)\)?

(A) \(\ \ -13\)
(B) \(\ \ 5 \)
(C) \(\ \ 105 \)
(D) \(\ \ 119 \)
(E) \(\ \ 131 \)

If \(h(x) = -x-3 ,\) for which of the following values of \(x\) is \(h(6x)=h(6+x)\)?

(A) \(\ \ -3\)

(B) \(\ \ -\frac{6}{7}\)

(C) \(\ \ -\frac{6}{5}\)

(D) \(\ \ 0\)

(E) \(\ \ \frac{6}{5}\)

If \(f(x)=\frac{3x^{2}-3x+28}{2x}\) and \(x\neq 0\), which of the following equals \(f(-7)\)?

(A) \(\ \ -14\)
(B) \(\ \ -7\)
(C) \(\ \ -2\)
(D) \(\ \ \ \ \ 11\)
(E) \(\ \ \ \ \ 14\)

A function \(f\) is even if for every \(x\) in the domain of \(f\), \(f(x)=f(-x)\). Which of the following functions is NOT even?

(A) \(\ \ f(x)=-x^{2}+2\)
(B) \(\ \ f(x) = 7\)
(C) \(\ \ f(x) = x+7\)
(D) \(\ \ f(x) = |7x|\)
(E) \(\ \ f(x) = 7x^{2}-2\)

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