1.) Let be defined by

Question

1.) Let be defined by

0

674

6

+109

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.) If $f(x)=\frac{x+4}{x^2+ax+b}$ and $f(x)$ has two vertical asymptotes at x=1 and x=-2, then find the sum of a and b.

dp1806 Aug 21, 2020

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Guest · Answer 1 · 2020-08-21T04:54:39

#1

0

1. f^{-1}(0) + f^{-1}(6) = 2 + 1 = 3.

2. a + b = (4) + (-2) = 2.

Guest Aug 21, 2020

#2

+109

-1

I appreciate that you've attempted to answer this question, however, both of your answers are wrong. I feel like you just picked some random numbers and showed some useless steps. But, this doesn't work. Sorry!!

dp1806 Aug 21, 2020

#5

+1094

+2

@geust, I'm not sure if you understand, but f^-1 means the inverse of the function, not f to the power of -1

:)

ilorty Aug 23, 2020

Alan · Answer 2 · 2020-08-21T07:27:43

#3

+33658

+1

This graph should help with question 1:

Alan Aug 21, 2020

#6

+1094

+2

If you can't see the picture, this link should work...https://web2.0calc.com/img/upload/86da579d92c1f599a70c4342/g0.jpg

im not sure why the image is blocked...

:)

ilorty Aug 23, 2020

Alan · Answer 3 · 2020-08-21T07:31:41

For question 2, the vertical asymptotes will occur where the denominator is zero. These will be where the roots of the denominator are. i.e. they will be such that (x + 2)(x - 1) = 0

Expand this and compare with x^2 + ax + b =0, to find a and b.

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