Explanation Given: u ( x ) = − x + 16 Inverse of a function: A function is defined as the relation formed between the independent variable ( x ) and the dependent variable ( y ) . Inverse of a function is also defined as the relation formed between the independent variable and the dependent variable. But it is formed by the independent variable ( x ) with the dependent variable ( y ) . The inverse of a function thus formed may or may not be a function. It is simply a relation. On the other hand if the inverse relation obtained by the above definition is itself also a function, then it is called as an inverse function. The inverse of a function is the set of ordered pairs which is obtained by interchanging the first and second element of each pair in the original function. In other words, we can tell that the inverse of a function is the set of ordered pairs which is obtained by interchanging x − a n d y − coordinates of each pair in the original function. Here the function is given as u ( x ) = − x + 16 . The domain of the given function is [ − 16 , ∞ ) .Range of the given function is ( − ∞ , 0 ] , because the range of a radical function of the form − c a x + b is f ( x ) ≤ k , as here k = 0 , f ( x ) ≤ 0 .The domain of the inverse function is ( − ∞ , 0 ] . Range of the inverse function is [ − 16 , ∞ ) .Here in this problem u ( x ) = − x + 16 with domain x ≥ − 16 is one to one, because it does satisfy the horizontal line test, this means that inverse is a function. We can say that the inverse function of f does exist. We have to find an equation of inverse of the given function, u − 1 ( x ) . For that first we have to write the given function u ( x ) . Then replace the term u ( x ) by y . Here we have to consider that if there any restriction is given for x then it automatically become as the restriction of y . After solving and simplifying we can obtain the value of y . In the final step, we have to change the term y by u − 1 ( x )

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ISBN: 9781264120697

Author: Miller

Publisher: MCG

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Chapter 8.2, Problem 64PE

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An equation of the inverse of the given one-to-one function

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Chapter 8.2, Problem 63PE

Chapter 8.2, Problem 65PE

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