Algebra Examples
f(x)=x+5f(x)=x+5
Step 1
Write f(x)=x+5f(x)=x+5 as an equation.
y=x+5y=x+5
Step 2
Interchange the variables.
x=y+5x=y+5
Step 3
Step 3.1
Rewrite the equation as y+5=xy+5=x.
y+5=xy+5=x
Step 3.2
Subtract 55 from both sides of the equation.
y=x-5y=x−5
y=x-5y=x−5
Step 4
Replace yy with f-1(x)f−1(x) to show the final answer.
f-1(x)=x-5f−1(x)=x−5
Step 5
Step 5.1
To verify the inverse, check if f-1(f(x))=xf−1(f(x))=x and f(f-1(x))=xf(f−1(x))=x.
Step 5.2
Evaluate f-1(f(x))f−1(f(x)).
Step 5.2.1
Set up the composite result function.
f-1(f(x))f−1(f(x))
Step 5.2.2
Evaluate f-1(x+5)f−1(x+5) by substituting in the value of ff into f-1f−1.
f-1(x+5)=(x+5)-5f−1(x+5)=(x+5)−5
Step 5.2.3
Combine the opposite terms in (x+5)-5(x+5)−5.
Step 5.2.3.1
Subtract 55 from 55.
f-1(x+5)=x+0f−1(x+5)=x+0
Step 5.2.3.2
Add xx and 00.
f-1(x+5)=xf−1(x+5)=x
f-1(x+5)=xf−1(x+5)=x
f-1(x+5)=xf−1(x+5)=x
Step 5.3
Evaluate f(f-1(x))f(f−1(x)).
Step 5.3.1
Set up the composite result function.
f(f-1(x))f(f−1(x))
Step 5.3.2
Evaluate f(x-5)f(x−5) by substituting in the value of f-1f−1 into ff.
f(x-5)=(x-5)+5f(x−5)=(x−5)+5
Step 5.3.3
Combine the opposite terms in (x-5)+5(x−5)+5.
Step 5.3.3.1
Add -5−5 and 55.
f(x-5)=x+0f(x−5)=x+0
Step 5.3.3.2
Add xx and 00.
f(x-5)=xf(x−5)=x
f(x-5)=xf(x−5)=x
f(x-5)=xf(x−5)=x
Step 5.4
Since f-1(f(x))=xf−1(f(x))=x and f(f-1(x))=xf(f−1(x))=x, then f-1(x)=x-5 is the inverse of f(x)=x+5.
f-1(x)=x-5
f-1(x)=x-5
