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


x+3 = 2

x = -1

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) = 2x(4x) = 8x^{2}

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

1 = Tany

From Trigonometry Value we know y = 45\degree