Which of the following functions has an inverse that is not a function? y = x y = 2x + 1 y = x²

ANSWER

EXPLANATION

For a function to be an invertible, it must be a one-to-one function.

In other words , it's graph should pass the horizontal line test.

It is obvious that,

and

will pass the horizontal line test.

But

has a v-shape and hence cannot pass the horizontal line test.

This means that y=x² is not invertible. That is, its inverse is not a function.

Let us quickly check that:

Interchange x and y.

Solve for y,

This is not a function, because it doesn't pass the vertical line test.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: