More practice college algrebra questions are presented with hints and answers. The "Submit" button at the bottom of the page will show which questions you answered incorrectly. You may go back to the questions you answered incorrectly and try again.
Q1) $z$ is a complex number and $\bar z$ its conjugate such that $2z-3\bar z=-2-5i$. What is $z$?
A. $2i$
B. $2+5i$
C. $2-i$
D. $1-2i$
E. $2+5i$
Remember that if $\bar z$ is the complex conjugate of $z$ and $z=a+ib$, then $\bar z = a-ib$.
Q2) If $f(x)=7-x^3$, what is the inverse function of $f(x)$?
A. $7-x$
B. $\dfrac{1}{7-x}$
C. $\sqrt[3]{7-x}$
D. $\sqrt[3]{x-7}$
E. $\sqrt[3]{7+x}$
Q3) If $\log_2 (4^a) = 5$, then a = ?
A. $5$
B. $2\dfrac{1}{2}$
C. $32$
D. $16$
E. $4$
Q4) Which of the following polynomial equations has the solution set {-4,-2,-1,0,4}?
A. $(x+2)(x+1)(x^2+16)=0$
B. $x(x+2)(x+1)(x^2-16)=0$
C. $(x+2)(x+1)(x-3)(x^2-16)=0$
D. $x(x+2)(x+1)(x^2+16)=0$
E. $x+(x+4)+(x+2)+(x+1)=0$
Q5) If $(3^{x^2})(9^{-3x})=\dfrac{1}{27^3}$, then $x=?$
A. $-3$
B. $9$
C. $3$
D. $1$
E. $-1$
Q6) If $h(x)=x^3-2$, then $h(h(0))=$?
A. $-2$
B. $8$
C. $-10$
D. $0$
Q7) If $(2x^2-3) \cdot f(x) = 2x^3-2x^2-3x+3$, then $f(x)=$
A. $x-1$
B. $x+1$
C. $x+3$
D. $2x+1$
E. $2x-3$
Q8) Function $f$ has its graph completely in Quadrant $II$. Where will the graph of the inverse function of $f$ be?
A. In quadrant $I$ and $II$
B. In quadrant $II$
C. In quadrant $III$
D. In quadrant $IV$
E. In quadrants $II$ and $III$
Q9) Which value of $k$ satiffies the equation $6! = 30(k!)$?
A. $8$
B. $6$
C. $4$
D. $2$
E. $0$
Q10) What are all the real values of $x$ for which $y$ defined by $y = \dfrac{1}{\sqrt{x^2-25}}$ is a real number?
A. $x>5$
B. $x \ge 5$
C. $x \le -5$ or $x \ge 5$
D. $-5 \lt x \lt 5$
E. $x \lt -5$ or $x \gt 5$
