College Algebra Practice Questions - Part 2

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. $2+5i$

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. $0$

E. $4$

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. $-5 < x < 5$

E. $x < -5$ or $x>5$