Answer: [tex]\bold{f^{-1}(-2)=-4\qquad f(-4)=-2\qquad f(f^{-1}(-2))=-2}[/tex]
Step-by-step explanation:
[tex]f(x)=\dfrac{1}{2}x\qquad \qquad \qquad \qquad f^{-1}(x)=2x\\\\\\f(-4)=\dfrac{1}{2}(-4)\qquad \qquad \qquad f^{-1}(-2)=2(-2)\\\\\\.\qquad =-2\qquad \qquad \qquad \qquad \qquad \qquad =-4[/tex]
[tex]f(f^{-1}(-2))\quad \rightarrow \quad f(-4)\quad = -2[/tex]
The value of f1(-2)f(-4) f(f-1(-2)) is -16.
The set of input values is called the domain of the function. And the set of output values is called the range of the function.
Given f(x) = 1/2x and f^-1(x)= 2x.
To solve for f1(-2) f(-4) f(f-1(-2)).
First of all ,
f(x) = 1/2x , f-1(x)= 2x
so, put x = 4, -4 in f(x) and put x=-2 in f^-1(x).
f(-4)=1/2(-4)
=> -2
f(4)=1/2(4)
=> 2
f^-1(-2)=2(-2)
=>-4
So, f(f-1(-2)) = f(-4) = -2
Now substitute all these values in the given expression of functions:
f1(-2) f(-4) f(f-1(-2)) = (-4)((-2)(-2)
=> -16.
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