Let f(x) = x + k (k is a constant).

**Step 1 :**

In the above function, f(x) has to be replaced by y.

Then, we will get

y = x + k

y = x + k has been defined by 'y' in terms of 'x'.

**Step 2 :**

Now we have to redefine y = x + k by 'x' in terms of 'y'.

Then we will get

x = y - k

**Step 3 : **

In x = y - k, replace 'x' by f^{-1}(x) and 'y' by 'x'.

Therefore, inverse of f(x) is,

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

**Example 1 :**

Find the inverse of the function f(x) = 2x + 3.

**Solution : **

**Step 1 :**

Given function : f(x) = 2x + 3

In the above function f(x) to be replaced by 'y'.

Then, we will get

y = 2x + 3

y = 2x + 3 has been defined by 'y' in terms of 'x'.

**Step 2 :**

Now we have to redefine y = 2x + 3 by 'x' in terms of 'y'.

y = 2x + 3

Subtract 3 from each side.

y - 3 = 2x

Divide each side by 2.

(y - 3) / 2 = x

x = (y - 3) / 2

Now, the function has been defined by 'x' in terms of 'y'.

**Step 3 : **

In x = (y - 3)/2, replace 'x' by f^{-1}(x) and 'y' by 'x'.

So, inverse of f(x) is,

f^{-1}(x) = (x - 3) / 2

**Example 2 : **

Find the inverse of the function h(x) = log_{10}(x).

**Solution : **

**Step 1 :**

Given function : h(x) = log_{10}(x)

In the above function h(x) to be replaced by 'y'.

Then, we will get

y = log_{10}(x)

y = log_{10}(x) has been defined by 'y' in terms of 'x'.

**Step 2 :**

Now we have to redefine y = log_{10}(x) by 'x' in terms of 'y'.

y = log_{10}(x)

10^{y} = x

x = 10^{y}

Now, the function has been defined by 'x' in terms of 'y'.

**Step 3 :**

In x = 10^{y} replace 'x' by h^{-1}(x) and 'y' by 'x'.

So, inverse of h(x) is,

h^{-1}(x) = 10^{x}

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