Question

inverse linear functions
example 2 write the inverse function of y = x + 9.
y - 9 = x + 9 - 9
y - 9 = x
x - 9 = y
the inverse function of y = x + 9 is y = x - 9.
example 3 write the inverse function of y = \frac{x}{-22}.
(-22)y=-\frac{x}{22}(-22)
-22y = x
-22x = y
the inverse function of y = \frac{x}{-22} is y = -22x.
write the inverse of each function.

1. y = x - 6
2. y = 7x
3. y = \frac{1}{2}x
4. y = x + 11
5. y = -18x
6. y = 21 + x

Explanation:

Step1: For \(y = x - 6\), isolate \(x\)

Add 6 to both sides: \(y+6=x\).

Step2: Switch \(x\) and \(y\)

The inverse function is \(y=x + 6\).

Step3: For \(y = 7x\), isolate \(x\)

Divide both sides by 7: \(x=\frac{y}{7}\).

Step4: Switch \(x\) and \(y\)

The inverse function is \(y=\frac{x}{7}\).

Step5: For \(y=\frac{1}{2}x\), isolate \(x\)

Multiply both sides by 2: \(2y=x\).

Step6: Switch \(x\) and \(y\)

The inverse function is \(y = 2x\).

Step7: For \(y=x + 11\), isolate \(x\)

Subtract 11 from both sides: \(y - 11=x\).

Step8: Switch \(x\) and \(y\)

The inverse function is \(y=x - 11\).

Step9: For \(y=-18x\), isolate \(x\)

Divide both sides by - 18: \(x=-\frac{y}{18}\).

Step10: Switch \(x\) and \(y\)

The inverse function is \(y=-\frac{x}{18}\).

Step11: For \(y = 21+x\), isolate \(x\)

Subtract 21 from both sides: \(y - 21=x\).

Step12: Switch \(x\) and \(y\)

The inverse function is \(y=x - 21\).

Answer:

1. \(y=x + 6\)
2. \(y=\frac{x}{7}\)
3. \(y = 2x\)
4. \(y=x - 11\)
5. \(y=-\frac{x}{18}\)
6. \(y=x - 21\)