Algebra Examples

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Algebra
Find the Inverse f(x)=x-9
f(x)=x-9
Step 1
Write f(x)=x-9 as an equation.
y=x-9
Step 2
Interchange the variables.
x=y-9
Step 3
Solve for y.
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Step 3.1
Rewrite the equation as y-9=x.
y-9=x
Step 3.2
Add 9 to both sides of the equation.
y=x+9
y=x+9
Step 4
Replace y with f-1(x) to show the final answer.
f-1(x)=x+9
Step 5
Verify if f-1(x)=x+9 is the inverse of f(x)=x-9.
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Step 5.1
To verify the inverse, check if f-1(f(x))=x and f(f-1(x))=x.
Step 5.2
Evaluate f-1(f(x)).
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Step 5.2.1
Set up the composite result function.
f-1(f(x))
Step 5.2.2
Evaluate f-1(x-9) by substituting in the value of f into f-1.
f-1(x-9)=(x-9)+9
Step 5.2.3
Combine the opposite terms in (x-9)+9.
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Step 5.2.3.1
Add -9 and 9.
f-1(x-9)=x+0
Step 5.2.3.2
Add x and 0.
f-1(x-9)=x
f-1(x-9)=x
f-1(x-9)=x
Step 5.3
Evaluate f(f-1(x)).
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Step 5.3.1
Set up the composite result function.
f(f-1(x))
Step 5.3.2
Evaluate f(x+9) by substituting in the value of f-1 into f.
f(x+9)=(x+9)-9
Step 5.3.3
Combine the opposite terms in (x+9)-9.
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Step 5.3.3.1
Subtract 9 from 9.
f(x+9)=x+0
Step 5.3.3.2
Add x and 0.
f(x+9)=x
f(x+9)=x
f(x+9)=x
Step 5.4
Since f-1(f(x))=x and f(f-1(x))=x, then f-1(x)=x+9 is the inverse of f(x)=x-9.
f-1(x)=x+9
f-1(x)=x+9
f(x)=x-9
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