Question

Use f(x) = 1/2 x and f -1(x) = 2x to solve the problems. f(2) = 1 f−1(1) = 2 f−1(f(2)) = 2 f−1(−2) = f(−4) = f(f−1(−2)) =

Answer 1

Answer:

In this problem, we are given the following functions:

$f(x)=\frac{1}{2}x$

and its inverse function:

$f^{-1}(x)=2x$

First of all, we want to calculate $f(2)$. This can be obtained by substituting

x = 2

into f(x). Doing so, we find:

$f(2)=\frac{1}{2}\cdot 2 = 1$

Then we want to calculate $f^{-1}(1)$. We can do it by substituting

x = 1

into $f^{-1}(x)$. Doing so,

$f^{-1}(1)=2\cdot 1 = 2$

Then we want to calculate $f^{-1}(f(2))$, which can be found by calculating f(2) and then using it as input for $f^{-1}(x).$ We know that

f(2) = 1

Therefore,

$f^{-1}(f(2))=f^{-1}(1)=2$

Then we want to calculate $f^{-1}(-2)$, which can be calculated by plugging

x = -2

into $f^{-1}(x)$. Doing so,

$f^{-1}(-2)=2\cdot (-2)=-4$

Then we want to calculate $f(-4)$; by substituting

x = 4

into f(x), we find

$f(-4)=\frac{1}{2}\cdot (-4)=-2$

Finally, we want to find $f(f^{-1}(-2))$

We know already that

$f^{-1}(-2)=-4$

So we have:

$f(f^{-1}(-2))=f(-4)=-2$

Answer 2

Answer:

f−1(−2) = -4

f(−4) = -2

f(f−1(−2)) = -2

Step-by-step explanation: