The inverse of f(x) is f^-1(x)=x/2+3.
Here, take y=f(x)
Then, y = 2x-6
⇒ 2x = y+6
⇒ x = y/2+6/2
⇒ x = y/2+3
Now, switch x and y in the above equation.
Then the resulting function of x is the inverse.
⇒ y = x/2 + 3
Then the inverse function is x/2+3.
Hence, option C is the correct inverse of the given function.
What is an inverse?
Inverse operationsare pairs of mathematical manipulations in which one operation undoes the action of the other—for example, addition and subtraction, multiplication and division. The inverse of a number usually means its reciprocal, i.e. x - 1 = 1 / x . The product of a number and its inverse (reciprocal) equals 1.
What is the inverse of 5?
1/5, Multiplicative Inverse of Natural Number
For example, the multiplicative inverse of 5 is 1/5
What is a inverse example?
Inverse operations are opposite operations that undo each other. For example, 5 ✕ 2 = 10 and 10 ÷ 2 = 5 are inverse operations.
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