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Methods to Discover Inverse of a Perform


The next steps can be helpful to search out inverse of a operate f(x), that’s f-1(x).

Step 1 : 

Substitute f(x) by y. 

Step 2 :

Interchange the variables x and y. 

Step 3 : 

Resolve for y.

Step 4 :

Substitute y by f-1(x). 

Instance 1 :

Discover the inverse of the operate f(x) = x – 5.

Answer :

f(x) = x – 5

Substitute f(x) by y.

y = x – 5

Interchange x and y. 

x = y – 5

Resolve for y.

y = x + 5

Substitute y by f-1(x).

f-1(x) = x + 5

Instance 2 :

Discover the inverse of the operate f(x) = 3x + 5.

Answer :

f(x) = 3x + 5

Substitute f(x) by y.

y = 3x + 5

Interchange x and y. 

x = 3y + 5

Resolve for y.

x – 5 = 3y

y = (x – 5)/3

Substitute y by f-1(x).

f-1(x) = (x – 5)/3

f-1 (x)  =  (x – 5)/3

Instance 3 :

Discover the inverse of the operate f(x) = x2.

Answer :

Substitute f(x) by y.

y = x2

Interchange x and y. 

x = y2

y2 = x

Resolve for y.

Take sq. root on either side. 

y = ±√x

Substitute y by f-1(x).

f-1(x) = ±√x

Instance 4 :

Discover the inverse of the operate f(x) = log5(x). 

Answer :

f(x) = log5(x)

Substitute f(x) by y.

y = log5(x)

Interchange x and y. 

x = log5(y)

Resolve for y.

y = 5x

Substitute y by f-1(x).

f-1(x) = 5x

Instance 5 :

Discover the inverse of the operate f(x) = √(x + 1). 

Answer :

f(x) = √(x + 1)

Substitute f(x) by y.

y = √(x + 1)

Interchange x and y. 

x = √(y + 1)

Resolve for y.

x2 = y + 1

y = x2 – 1

Substitute y by f-1(x).

f-1(x) = x2 – 1

Instance 6 :

Discover the inverse of the operate f(x) = (x + 2)/(x – 5). 

Answer :

f(x) = (x + 2)/(x – 5)

Substitute f(x) by y.

y = (x + 2)/(x – 5)

Interchange x and y. 

x = (y + 2)/(y – 5)

Resolve for y.

x(y – 5) = y + 2

xy – 5x = y + 2

xy – y = 5x + 2

y(x – 1) = 5x + 2

y = (5x + 2)/(x – 1)

Substitute y by f-1(x).

f-1(x) = (5x + 2)/(x – 1)

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