Math

QuestionFind the inverse of the function Q(x)=2x74Q(x)=\frac{2 x-7}{4}. Show all work.

Studdy Solution

STEP 1

Assumptions1. The function is given as Q(x)=x74Q(x)=\frac{x-7}{4}. . We are asked to find the inverse of this function, denoted as Q1(x)Q^{-1}(x).

STEP 2

To find the inverse of a function, we first replace the function notation Q(x)Q(x) with yy.
y=2x74y = \frac{2x-7}{4}

STEP 3

The next step in finding the inverse of a function is to swap xx and yy. This means we replace every xx with yy and every yy with xx.
x=2y7x = \frac{2y-7}{}

STEP 4

Now, we solve this equation for yy to get the inverse function. First, multiply both sides of the equation by4 to get rid of the denominator.
4x=2y74x =2y -7

STEP 5

Next, add7 to both sides of the equation to isolate the term with yy.
4x+7=2y4x +7 =2y

STEP 6

Finally, divide both sides of the equation by2 to solve for yy.
y=4x+2y = \frac{4x+}{2}

STEP 7

Now that we have solved for yy, we can write the inverse function. We replace yy with Q1(x)Q^{-1}(x) to denote the inverse function.
Q1(x)=4x+72Q^{-1}(x) = \frac{4x+7}{2}So, the inverse of the function Q(x)=2x74Q(x)=\frac{2x-7}{4} is Q1(x)=4x+72Q^{-1}(x) = \frac{4x+7}{2}.

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