+0

0
211
2

1. Let $f$ be defined by $f(x) = \left\{ \begin{array}{cl} 3-x & \text{ if } x \leq 3, \\ -x^3+2x^2+3x & \text{ if } x>3. \end{array} \right.$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

#1
+98044
+1

2.

$$y=\frac{x-2}{x^2-7x+10}$$

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

Apr 25, 2018
#2
+98044
+1

3.

$$\sqrt{5 + x} + \sqrt{20 - x} = 7$$

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

So

(5 + 4) (20 - 4)   =

9 * 16 =

144

Apr 26, 2018