CLEP College Algebra Practice Questions -- Functions and their properties

1. If $f(x)=-x^{3}+2x+1$ what is $f(-3x)$
   
   
   1. $27x^{3}-6x+1$
   2. $-27x^{3}-6x+1 $
   3. $-27x^{3}+6x+1 $
   4. $27x^{3}-6x-1 $
   5. $-3x^{3}-6x+1 $
   
   
2. If $f(x)=9x+3$ then $f^{-1}(x)=$
   
   
   1. $\frac{1}{9}x-\frac{1}{3}$
   2. $\frac{1}{3}+\frac{1}{9} $
   3. $9x-3 $
   4. $\frac{1}{3}x+1 $
   5. $x-\frac{1}{9} $
   
   
3. If $f(x,y)=\frac{x \log x}{y \log y}$ then $f(8,2)=$
   
   
   1. $4$
   2. $24 $
   3. $ \frac{3}{2}$
   4. $\log 2 $
   5. $12 $
   
   
4. $\log_{5}(\frac{1}{125})$
   
   
   1. $\frac{1}{3}$
   2. $-\frac{1}{3} $
   3. $5 $
   4. $3 $
   5. $-3 $
   
   
5. The function $f$ is defined by $f(x)=\frac{1}{1-x}$. For what values of $x$ is $f(f(x))$ undefined?
   
   
   1. $\{0\}$
   2. $\{1\} $
   3. $\{-1,2\} $
   4. $\{0,1\} $
   5. $\{-1,0\} $
   
   
   
   
6. If $f(x)=\frac{7x-5}{2}$, find the solution set for $f(x)>3x$
   
   
   1. $\{x/ x>5 \}$
   2. $\{x/ x<5 \} $
   3. $\{ x/ x>3 \} $
   4. $\{ x/ x \leq -3 \} $
   5. None of the above
   
   
7. If $f(x)=3x+7$ and $g(x)=2x-1$, what is $f(g(1))$?



8. Find the equation for the line passing through $(4,2)$ and $(-1,3)$
   
   
   1. $5y-x=14$
   2. $5y+x=-14$
   3. $-5y+x=14$
   4. $y+5x=14$
   5. $5y+x=14$
   
   
9. Solve $2^{7x}=4^{2x-1}$
   
   
   1. $\frac{2}{3}$
   2. $\frac{3}{2}$
   3. $-\frac{2}{3}$
   4. $3$
   5. $\frac{2}{3}$
   
   
10. Find $\log_{3} 81$
    

Answer Key

1	A
2	A
3	E
4	E
5	D
6	A
7	10
8	E
9	C
10	4