Let f(x) = 2x - 6. Solve f^-1(x) when x = 2.

Solution:

Given f(x) = 2x - 6

A function is defined as a relationship between one variable (the independent variable) and another variable (the dependent variable)

Let y = 2x - 6

Given that, f(x) = 2x − 6.

Let, y = f(x) = 2x − 6.

Solve for x in terms of y, to get inverse of a function f ^-1(x).

⇒ y = 2x - 6

⇒ y + 6 = 2x

⇒ x = y/2 + 3

which means, f ^-1(x) = x/2 + 3.

Substituting x = 2,

⇒ f ^-1(2) = 2/2 + 3

⇒ f ^-1(2) = 1 + 3

⇒ f ^-1(2) = 4

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Let f(x) = 2x - 6. Solve f^-1(x) when x = 2.

Summary:

If f(x) = 2x - 6 then the value of f^-1(x) is 4 when x = 2.