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Trigonometry Examples
f(x)=20x
Step 1
Write f(x)=20x as an equation.
y=20x
Step 2
Interchange the variables.
x=20y
Step 3
Step 3.1
Rewrite the equation as 20y=x.
20y=x
Step 3.2
Divide each term in 20y=x by 20 and simplify.
Step 3.2.1
Divide each term in 20y=x by 20.
20y20=x20
Step 3.2.2
Simplify the left side.
Step 3.2.2.1
Cancel the common factor of 20.
Step 3.2.2.1.1
Cancel the common factor.
20y20=x20
Step 3.2.2.1.2
Divide y by 1.
y=x20
y=x20
y=x20
y=x20
y=x20
Step 4
Replace y with f−1(x) to show the final answer.
f−1(x)=x20
Step 5
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)).
Step 5.2.1
Set up the composite result function.
f−1(f(x))
Step 5.2.2
Evaluate f−1(20x) by substituting in the value of f into f−1.
f−1(20x)=20x20
Step 5.2.3
Cancel the common factor of 20.
Step 5.2.3.1
Cancel the common factor.
f−1(20x)=20x20
Step 5.2.3.2
Divide x by 1.
f−1(20x)=x
f−1(20x)=x
f−1(20x)=x
Step 5.3
Evaluate f(f−1(x)).
Step 5.3.1
Set up the composite result function.
f(f−1(x))
Step 5.3.2
Evaluate f(x20) by substituting in the value of f−1 into f.
f(x20)=20(x20)
Step 5.3.3
Cancel the common factor of 20.
Step 5.3.3.1
Cancel the common factor.
f(x20)=20(x20)
Step 5.3.3.2
Rewrite the expression.
f(x20)=x
f(x20)=x
f(x20)=x
Step 5.4
Since f−1(f(x))=x and f(f−1(x))=x, then f−1(x)=x20 is the inverse of f(x)=20x.
f−1(x)=x20
f−1(x)=x20