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1. Let $f$ be defined by f(x)={3−x if x≤3,−x3+2x2+3x if x>3.Calculate $f^{-1}(0)+f^{-1}(6)$.

2. For how many values of $x$ is the function $y=\frac{x-2}{x^2-7x+10}$ not defined?

3. If $\sqrt{5 + x} + \sqrt{20 - x} = 7$, what is the value of $(5 + x)(20 - x)$?

 Apr 25, 2018

2+0 Answers

 #1
avatar+130466 
+1

2.

 

y=x−2x2−7x+10

 

Factor the denominator

 

y =        (x - 2)

     ___________    

       (x - 2) (x - 5)

 

This will not be defined  for any values that make the denominator  0

 

Thus....it will not be defined when x  = 2   or  x = 5

 

Thus.....two values

 

 

cool cool cool

 Apr 25, 2018
 #2
avatar+130466 
+1

3. 

 

√5+x+√20−x=7

 

We probably can  just solve this by inspection....note.....x = 4 seems to work

 

So

 

(5 + 4) (20 - 4)   =  

 

9 * 16 =

 

144

 

 

cool cool cool

 Apr 26, 2018

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