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) = x^{2}.

Answer :

Substitute f(x) by y.

y = x^{2}

Interchange x and y.

x = y^{2}

y^{2} = 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) = log_{5}(x).

Answer :

f(x) = log_{5}(x)

Substitute f(x) by y.

y = log_{5}(x)

Interchange x and y.

x = log_{5}(y)

Resolve for y.

y = 5^{x}

Substitute y by f^{-1}(x).

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

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.

x^{2} = y + 1

y = x^{2} – 1

Substitute y by f^{-1}(x).

f^{-1}(x) = x^{2} – 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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