Question

(a) f(x) = f (1-x)
(b) f(x) + f(1-x) =0
(c) f(x) + f(1-x) =1
(d) f(x) + f (1-x) = 1

please answer with proper solution...​

Answer 1

STEP 1: Stick a "y" in for the "f(x)" guy:

y = -( 1 / 3 )x + 1

STEP 2: Switch the x and y

( because every (x, y) has a (y, x) partner! ):

x = -( 1 / 3 )y + 1

STEP 3: Solve for y:

x = -( 1 / 3 )y + 1 ... multiply by 3 to ditch the fraction ... 3x = -y + 3 ... ditch the +3 ... subtract 3 from both sides ... 3x - 3 = -y ... multiply by -1 ... -3x + 3 = y ... y = -3x + 3

STEP 4: Stick in the inverse notation, f^( -1 )( x )

f^( -1 )( x ) = -3x + 3