Inverse Functions: f(x) = 2x − 4, x > 0; −3x + 1 otherwise

[HugeLag]

f(x) is defined over the real number set R as follows:

f(x) = 2x − 4 x > 0
−3x + 1 otherwise

Determine f(0), f(−1), f(1), f(5/2),f^-1(0)

f(0) = -1
f(-1) = 2
f(1) = -2
f(5/2) = 1
f^-1(0) = Can someone explain how to work this out? Also the place where I am trying to input this only accepts numerical values not x's. So i dont think the answer can be anything over x.

I got all of these correct so far however I am really struggling to understand how to work out f^-1(0)

 

[Deleted member 4993]

f(x) is defined over the real number set R as follows:

f(x) = 2x − 4 x > 0
−3x + 1 otherwise

Determine f(0), f(−1), f(1), f(5/2),f^-1(0)

f(0) = -1
f(-1) = 2
f(1) = -2
f(5/2) = 1
f^-1(0) = Can someone explain how to work this out? Also the place where I am trying to input this only accepts numerical values not x's. So i dont think the answer can be anything over x.

I got all of these correct so far however I am really struggling to understand how to work out f^-1(0)

Can you define f^-1(x) in those domains? Also plot the inverse function? Is it continuous?

 

[pka]

f(x) is defined over the real number set R as follows:
f(x) = 2x − 4 x > 0
−3x + 1 otherwise
Determine f(0), f(−1), f(1), f(5/2),f^-1(0)
I got all of these correct so far however I am really struggling to understand how to work out f^-1(0)

\(\displaystyle f(x)=\begin{cases}2x-4 & x>0 \\ -3x+1 & \text{else}\end{cases}\)
Can you find an \(\displaystyle a\) such that \(\displaystyle f(a)=0~?\)
If you can then \(\displaystyle f^{-1}(0)=a\).

 

[Steven G]

f(x) is defined over the real number set R as follows:

f(x) = 2x − 4 x > 0
−3x + 1 otherwise

Determine f(0), f(−1), f(1), f(5/2),f^-1(0)

f(0) = -1 Nope
f(-1) = 2 Nope
f(1) = -2 Yes
f(5/2) = 1 Yes
f^-1(0) = Can someone explain how to work this out? Also the place where I am trying to input this only accepts numerical values not x's. So i dont think the answer can be anything over x.

I got all of these correct so far however I am really struggling to understand how to work out f^-1(0)

You should first learn how to evaluate using a piecewise function, as you got half of the problems wrong, before going onto finding inverse.