Math/Inverse assignment/ algebra 1

Question

PLEASE ANSWER!

Find the inverse for each relation

1. {(1,‐2), (2, 3),(3, ‐3),(4, 2)}

2.. {(4,2),(5,1),(6,0),(7,‐1)}

Find an equation for the inverse for each of the following relations.

3.y=-8x+3

4.y=2/3x-5

5.y=1/2x+10

6.y=(x-3)^2

Verify that f and g are inverse functions.

7.f(x)=5x+2;g(x)=(x-2)/5

8.f(x)=1/2x-7;g(x)=2x+14

Answer 1

for 1) and 2) just switch the x and y coordinates.

1) (1,-2)'s inverse is (-2,1)

3) through 6) just switch x and y in the equation, then solve for the new y

3) y=-8x+3 becomes x=-8y+3

then solve for the new y

-8y =x -3

y=-x/8+3/8

or

y = (-x+3)/8

or

y =(3-x)/8

f^-1(x) = -x/8 + 3/8 is the inverse function of f(x) = -8x+3

7) and 8) calculate f(g(x)) or g(f(x)) and show it = x

7) f(x) = 5x+2, g(x) = (x-2)/5

f(g(x)) = 5((x-2)/5) +2 = x-2 +2 = x