Piecewise Function: f(x) = x^2+2x for 0<=x<=5, 3x-2 for -3<=x<0; g(x) = 1-4x

[lyndzkd]

Piecewise Function: f(x) = x^2+2x for 0<=x<=5, 3x-2 for -3<=x<0; g(x) = 1-4x

Hey everyone, I've been trying to figure this problem out for hours now!

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18) Let \(\displaystyle \,f(x)\, =\, \begin{cases}x^2\, +\, 2x & \mbox{if }\, 0\, \leq\, x\, \leq\, 5 \\ 3x\, -\, 2 & \mbox{if }\, -3\, \leq\, x\, <\, 0 \end{cases}\,\) and \(\displaystyle \,g(x)\, =\, 1\, -\, 4x\)

. . . . .Find:
. . . . .(a) f (0)
. . . . .(b) f (-1)
. . . . .(c) f (4) - f (-2)
. . . . .(d) f (g (0))
. . . . .(e) g (f (0))

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Can anyone help? Thank you!!

 

[Deleted member 4993]

Hey everyone, I've been trying to figure this problem out for hours now! Can anyone help? Thank you!!
View attachment 7914

What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33

 

[stapel]

Hey everyone, I've been trying to figure this problem out for hours now!

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18) Let \(\displaystyle \,f(x)\, =\, \begin{cases}x^2\, +\, 2x & \mbox{if }\, 0\, \leq\, x\, \leq\, 5 \\ 3x\, -\, 2 & \mbox{if }\, -3\, \leq\, x\, <\, 0 \end{cases}\,\) and \(\displaystyle \,g(x)\, =\, 1\, -\, 4x\)

. . . . .Find:
. . . . .(a) f (0)
. . . . .(b) f (-1)
. . . . .(c) f (4) - f (-2)
. . . . .(d) f (g (0))
. . . . .(e) g (f (0))

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Can anyone help?

Certainly we can help! But first we'll need to see at least sample results of your hours of efforts. You plugged the given values into the given functions, simplified, and... then what? Where are things going sideways?

Please be complete. Thank you!

 

[HallsofIvy]

Do you you do not understand what such a definition means? Rather than doing that specific problem (it is far better for you to do it- and it is not at all hard once you understand the notation) I will give a different example.

Suppose f is defined by \(\displaystyle f(x)= \left\{\begin{array}) x^2- 7 & x< -1 \\ 3x- 4 & -1\le x\le 5 \\ x^3+ 4 & 5< x \end{array}\right\}\)

What is f(-6)? I first note that -6< -1 so the first row applies: \(\displaystyle f(-6)= (-6)^2- 7= 29\).
What is f(0)? I first note that 0 is between -1 and 5 so the second row applies: \(\displaystyle f(0)= 3(0)- 4= -4\).
What is f(7)? I first note that 7 is larger than 5 so the third row applies: \(\displaystyle f(7)= 7^3+ 4= 347\).
What is f(-1)? I first note that the first row says "less than -1" and the second says "greater than or equal to -1" so the second row applies: \(\displaystyle f(-1)= 3(-1)+ 4= 1\).
What is f(5)? Again the second row says "less than or equal to 5" while the third row says "greater than 5" so the second row still applies: \(\displaystyle f(5)= 3(5)+ 4= 19\).