Step-by-step explanation:
A: f(x)=8x-2
1. Switch the f(x) to y
y=8x-2
2. Switch y to x and x to y
x=8y-2
3. Solve for y:
------------------------------
1. Add 2 to both sides.
x=8y-2
+2 +2
2. Divide both sides by 8.
x+2=8y
--- ---
8 8
1/8x+1/4=y
3. Write in f-inverse form
f^-1(x)=1/8x+1/4
B: g(x)=2/3x+6
1. Switch the g(x) to y
y=2/3x+6
2. Switch y to x and x to y
x=2/3y+6
3. Solve for y:
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1. Subtract 6 from both sides.
x=2/3y+6
-6 -6
2. Multiply both sides by 3/2 (to cancel out the 2/3)
x-6=2/3y
2/3x-4=y
3. Write in f-inverse form
g^1(x)=2/3x-4
C: h(x)-4x-12
1. Switch the h(x) to y
y=-4x-12
2. Switch y to x and x to y
x=-4y-12
3. Solve for y:
------------------------------
1. Add 12 to both sides.
x=-4y-12
+12 +12
2. Divide both sides by -4
x+12=-4y
------ ---
-4 -4
-1/4x-3=y
3. Write in h-inverse form
h^2(x)=-1/4/x-3
