Question

What is the inverse of the function f(x) =2x-10

Answer 1

$f(x) =2x-10 \\ y=2x-10 \\ \\ x = 2y-10 \\ 2y = x+10 \\ y= \frac{1}{2} x+5 \\ \\ \\ \boxed {f^{-1}(x)= \frac{1}{2} x+5}$

Answer 2

The inverse of the ƒunction f(x) =2x-10  

$\large{\boxed{\bold{f^{-1}(x)~=~\frac{1}{2}x~+~5}}}$  

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)  

• 2. f⁻¹(y) = g(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  

$x~=~\frac{y+10}{2}$  

$x~=~\frac{1}{2}y~+~5$  

$f^{-1} (y)~=~\frac{1}{2}y~+~5$  

so that  

$f^{-1}(x)~=~\frac{1}{2}x~+~5$  

Learn more  

the ƒunction has an inverse ƒunction  

brainly.com/question/12333704  

the inverse of the ƒunction  

brainly.com/question/9289171  

the inverse of a ƒunction always a ƒunction  

brainly.com/question/2873333  

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Keywords: ƒunction, inverse ƒunction, arrow diagrams