Which of the is the inverse of (\f(x) = 4x+12\)?
Answers
Answered by
5
Find the Inverse Function f(x)=4x-12
f(x)=4x−12f(x)=4x-12
Replace f(x)f(x) with yy.
y=4x−12y=4x-12
Interchange the variables.
x=4y−12x=4y-12
Solve for yy.
Since yy is on the right side of the equation, switch the sides so it is on the left side of the equation.
4y−12=x4y-12=x
Add 1212 to both sides of the equation.
4y=12+x4y=12+x
Divide each term by 44 and simplify.
Divide each term in 4y=12+x4y=12+xby 44.
4y4=124+x44y4=124+x4
Reduce the expression by cancelling the common factors.
Cancel the common factor.
4y4=124+x44y4=124+x4
Divide yy by 11.
y=124+x4y=124+x4
Divide 1212 by 44.
y=3+x4y=3+x4
Solve for yy and replace with f−1(x)f-1(x).
Replace the yy with f−1(x)f-1(x)to show the final answer.
f−1(x)=3+x4f-1(x)=3+x4
Set up the composite result function.
f(g(x))f(g(x))
Evaluate f(g(x))f(g(x)) by substituting in the value of gg into ff.
4(3+x4)−124(3+x4)-12
Simplify each term.
Apply the distributive property.
f(3+x4)=4⋅3+4(x4)−12f(3+x4)=4⋅3+4(x4)-12
Multiply 44 by 33.
f(3+x4)=12+4(x4)−12f(3+x4)=12+4(x4)-12
Cancel the common factor of 44.
Write 44 as a fraction with denominator 11.
f(3+x4)=12+41⋅x4−12f(3+x4)=12+41⋅x4-12
Factor out the greatest common factor 44.
f(3+x4)=12+4⋅11⋅x4⋅1−12f(3+x4)=12+4⋅11⋅x4⋅1-12
Cancel the common factor.
f(3+x4)=12+4⋅11⋅x4⋅1−12f(3+x4)=12+4⋅11⋅x4⋅1-12
Rewrite the expression.
f(3+x4)=12+11⋅x1−12f(3+x4)=12+11⋅x1-12
Simplify.
Multiply 1111 and x1x1.
f(3+x4)=12+x1−12f(3+x4)=12+x1-12
Divide xx by 11.
f(3+x4)=12+x−12f(3+x4)=12+x-12
Simplify by subtracting numbers.
Subtract 1212 from 1212.
f(3+x4)=x+0f(3+x4)=x+0
Add xx and 00.
f(3+x4)=xf(3+x4)=x
Since f(g(x))=xf(g(x))=x, f−1(x)=3+x4f-1(x)=3+x4 is the inverse of f(x)=4x−12f(x)=4x-12.
f−1(x)=3+x4
Answered by
3
The inverse of f(x) = 4x + 12 is given by
Given : The given function f(x) = 4x + 12
To find : The inverse of the function
Solution :
Here the given function is
f(x) = 4x + 12
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