INVERSE FUNCTION

Question 1

A RELATION REVERSING THE PROCESS PERFORMED BY ANY FUNCTION f(x) IS CALLED INVERSE OF f(x).

Answer 1

INVERSE FUNCTION

Question 2

TO TEST IF INVERSE FUNCTION IS A FUNCTION ?

Answer 2

VERTICAL AND HORIZONTAL LINE TEST

Question 3

HOW TO FIND f-1(x) ?

Answer 3

> REPLACE f(x) WITH Y
INTERCHANGE X AND Y
SOLVE FOR THE NEW Y FROM THE EQUATION IN STEP 2.
REPLACE THE NEW Y WITH f-1(x) IF THE INVERSE IS A FUNCTION.

Question 4

HOW TO FIND f-1(x) ?

Answer 4

> REPLACE f(x) WITH Y
INTERCHANGE X AND Y
SOLVE FOR THE NEW Y FROM THE EQUATION IN STEP 2.
REPLACE THE NEW Y WITH f-1(x) IF THE INVERSE IS A FUNCTION.

Question 5

f(x) = 3x + 6
y = 3x + 6
x = 3y + 6
-3y = -x + 6
-3y        -3
y = -x / -3 + 6 / -3
y = x/3 -2
f-1(x) = 1/3x - 2

Answer 5

> REPLACE f(x) WITH Y
INTERCHANGE X AND Y
SOLVE FOR THE NEW Y FROM THE EQUATION IN STEP 2.
REPLACE THE NEW Y WITH f-1(x) IF THE INVERSE IS A FUNCTION.

Question 6

f(x) = 2X + 5 AND g(x) = 1/2 (x-5)
PROVING f[g(x)] = x
f[g(x)] = f[1/2(x-5)]
f(x) = 2x + 5

f[g(x)] = 2[1/2 (x-5)] +5
f[g(x)] = 2(x-5/2) + 5
f[g(x)] = x - 5 + 5
f[g(x)] = x

Answer 6

f(x) = 2X + 5 AND g(x) = 1/2 (x-5)
PROVING g[f(x)] = x
g[f(x)] = g[2x + 5]
g(x) = 1/2 (x-5)

g[f(x)] = 1/2 (2x + 5 - 5)
g[f(x)] = 1/2 (2x)
g[f(x)] = 2X/2
g[f(x)] = x