Question

Find the domain and range of f-1 given f (x) =x-921-4x

Answer 1

The function given is

$f^{-1}(x)=\frac{x-9}{21-4x}$

The domain is the set of x-values for which a function is defined.

The range is the set of y-values for which a function is defined.

This is a rational function, so it has asymptotes, lines which a function approaches, but doesn't touch.

For domain,

we equate denominator equal to 0 and find the value of x that makes the function undefined. This is excluded from the domain.

$\begin{gathered} 21-4x=0 \\ 4x=21 \\ x=\frac{21}{4} \end{gathered}$

For range,

This is a rational function where the x-axis is an asymptote.

Thus, x = 0 is excluded from the range.

So, we can say:

Domain = (-∞, 21/4) U (21/4, ∞)Range = (-∞, 0) U (0, ∞)

First answer choice is right.