Determine wheather each pair of functions are inverse functions f(x) -2x+3 g(x) -1/2x+3/2

Answer 1

You can plug g(x) in for x in the f(x) equation. If it reduces to x, then they are inverses.

f(x) = -2 (g(x)) +3

f(x) = -2 (-1/2x+ 3/2)+ 3

simplify

f(x) = x-3+3

f(x) = x

Or you can calculate the inverse yourself.

f(x) = -2x + 3

write as

y = -2x + 3

exchange places of the x and y

x = -2y + 3

solve for y

x-3 = 2y

y = 1/2x - 3/2

Since this is the g(x) you were given, f(x) and g(x) are inverse functions.