QUESTION 1
The given function is;
This is an absolute value function.
For this function to have an inverse it must be a one-to-one function.
This absolute value function is not one-to-one
because
and
Since this function has more than one x-value mapping onto one y-value, it is not one-to-one and cannot have an inverse.
You can see from the graph that this function cannot pass the horizontal line test.
QUESTION 2
The given function is
Let
This implies that,
We see clearly that, this function is a circle that is centered at the origin.
This means that,
is a semicircle.
This function will not pass the horizontal line test and hence does not have an inverse.
QUESTION 3
The given function is
If we put
We obtain,
This shows that h(x) has an inverse because it is one-to-one.
Let
We interchange x and y to get,
Group like terms to get,
Factor to get,
Solve for y,
Hence
where
The given function is;
This is an absolute value function.
For this function to have an inverse it must be a one-to-one function.
This absolute value function is not one-to-one
because
and
Since this function has more than one x-value mapping onto one y-value, it is not one-to-one and cannot have an inverse.
You can see from the graph that this function cannot pass the horizontal line test.
QUESTION 2
The given function is
Let
This implies that,
We see clearly that, this function is a circle that is centered at the origin.
This means that,
is a semicircle.
This function will not pass the horizontal line test and hence does not have an inverse.
QUESTION 3
The given function is
If we put
We obtain,
This shows that h(x) has an inverse because it is one-to-one.
Let
We interchange x and y to get,
Group like terms to get,
Factor to get,
Solve for y,
Hence
where