What is the domain and range for $y = 6sin^-1(4x)$ ?

Question

4999 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-07-28T11:36:45

domain : $-1/4<=x<=1/4$

range : $yinRR$

Remember simply that the domain of any function are the values of $x$ and the range is the set of values of $y$

Function : $y=6sin^-1(4x)$

Now, rearrange our function as : $y/6=sin^-1(4x)$

The corresponding $sin$ function is $sin(y/6)=4x$ then $x=1/4sin(y/6)$

Any $sin$ function oscillates between $-1$ and $1$

$=>-1<=sin(y/6)<=1$

$=>-1/4<=1/4sin(y/6)<=1/4$

$=>-1/4<=x<=1/4$

Congratulations you have just found the domain(the values of $x$ )!

Now we proceed to find the values of $y$ .

Starting from $x=1/4sin(y/6)$

We see that any real value of $y$ can satisfy the above function.

Meaning that $y in RR$

What is the domain and range for y = 6sin^-1(4x)y = 6sin^-1(4x)?