Inverse Questions and Answers

y= 4x+20

x= 4y+20

x—20 = 4y

y= \frac{x-20}{4}

f(x) = x + 12

y = x + 12

x = y +12

y = x -12

f^{-1} (x) = x -12

 

g(x) = \frac{1}{2}x+ 4

y= \frac{1}{2}x+ 4

x = \frac{1}{2}y+ 4

2x = y + 8

y = 2x - 8

g^{-1}(x) = 2x -8

If f is an inverse function denoted by f^{-1}


f^{-1} ,= (y) = x, if and only if f(x) = y

 

y = 32x +5

x = 32y +5

y = \frac{x-5}{32}

(x + 3)4 - 8 = y


4x+12 - 8  = y

4x + 4 = y

4y + 4 = x

y = (x-4)/4

f(x) = 3x + 5

y = 3x + 5

x = 3y + 5

3y = x - 5


y = \frac{x -5}{3}


Hence, f^{-1} = \frac{x -5}{3}

y = 27 - 4x

x = 27 -4y

4y = 27 - x

y = \frac{27-x}{4}

f(-1) = 0

f (0) =1

f(1) =2

It means

 g (0) = -1,

g(1) = 0

g(2) = 1

 x = \frac{1}{y}

Interchanging variables, we get

y = \frac{1}{x}

Hence, f^{-1} = \frac{1}{x}

y = 3x+9

x=3y+9

x-9 =3y

y = \frac{x-9}{3}

f^{-1}(x) = 4x+5

f^{-1}(5) = 4\times 5 + 5 =25

y = Sin(x)

x = sin(y)

y = sin^{-1}(x)

 

Let y = Sin^{-1}(\frac{1}{2})

\frac{1}{2} = siny

From Trigonometry Value we know y = 30\degree

y = 7x

x = 7y

y = \frac{1}{7}\times x

 

f(g(x))= f(4x) = 2(4x)= 8x 

Let y = Tan^{-1}(1)

1 = Tany

From Trigonometry Value we know y = 45\degree

f(x) = 23x + 34

f(2) = 23\times 2 + 34 = 46 + 34 = 80

 

f^{-1}(x) = 3x^{2} + 4x +7

f^{-1}(2) = 3\times 2^{2} + 4\times 2 +7  = 27

 

(2x + 3)3 - 6 = y

(6x + 9) - 6 = y

(6x + 3)  = y

6y + 3 = x

y = (x -3)/6

f(4) = 6 , f(7) = 9 , f(2) =4

It means g(6) = 4 , g(9) = 7 ,g(4) = 2

 

From Property of Inverse trigonometric Functions

Value of tan^{-1}(\frac{1}{x}) = cot^{-1}(x)

 

From Property of Inverse trigonometric Functions

Value of cos^{-1}(cos\theta) = \theta

f(1) = 1 , f(2) = 4 , f(3) =9

It means g(1) = 1 , g(4) = 2 ,g(9) = 3

So g(4) = 2

f(x) = 33x - 6 = 33\times 4 - 6 = 126

y = \frac{2x+3}{3}

x = \frac{2y+3}{3}

3x = 2y + 3

2y = 3x - 3

y=\frac{3x-3}{2}

 

cos^{-1}(1) = 0\degree

f(x) = 4x^{2} + 3x = 4\times 3^{2} + 3\times 3 = 36 +9 = 45

(4x + 3)7 - 28 = y

28x + 21 -28 = y

28x  - 7 = y

28y - 7 =x

y = (x + 7) / 28

f(g(x)) = f(2x) = 7x(2x) = 14x^{2}