The inverse of the ƒunction f(x) =2x-10
[tex]\large{\boxed{\bold{f^{-1}(x)~=~\frac{1}{2}x~+~5}}}[/tex]
Further explanation
Set A to set B is said to be a ƒunction if each member of set A pairs exactly one member of set B
So, one value of x is only assigned to one value of y
A ƒunction can be expressed in the form of a cartesian diagram, sequential pairs, or arrow diagrams
If a ƒunction (f) pairs members of set A to set B, then the inverse of ƒunction f (f⁻¹) pairs members of set B to A, or easily f⁻¹ is the opposite of f
or in the form of equations
f (x) = y if and only if g (y) = x
g (y) is called the inverse of f (x)
The step for determining the inverse ƒunction
- 1. expresses the ƒunction y = f (x) in the form x = f (y)
- 3. Replace the letter y with x so we get the inverse ƒunction formula f⁻¹(x)
Known :
f (x) = 2x-10
suppose f (x) = y then
y = 2x-10
2x = y + 10
[tex]x~=~\frac{y+10}{2}[/tex]
[tex]x~=~\frac{1}{2}y~+~5[/tex]
[tex]f^{-1} (y)~=~\frac{1}{2}y~+~5[/tex]
so that
[tex]f^{-1}(x)~=~\frac{1}{2}x~+~5[/tex]
Learn more
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Keywords: ƒunction, inverse ƒunction, arrow diagrams
