Can anyone help me solve this Pre Calc problem?

Question

Directions: Find the domain of the function using exact form (no decimal approximations) and completely reduced.

Function: f(x)= {10th root of (7x-1)} / {4th root of (5-3x)}



basically i have to restrict what x can equal. one answer i've gotten already is that x cannot equal -5/3, but i'm pretty sure there's at least one more answer...

ok ya i messed up the sign on that.
so one answer is 5/3.
i think the other answer is x is > or = to -1/7 ?

Answer 1

This is not as difficult as it looks. Since your function is a fraction, the only restriction you have is that denominator cannot be equal to zero.

So you will be solving y= {4th root of (5-3x)}

What can x NOT be, so that y would not equal to zero?

0=4th sqrt of (5-3x)
0=5-3x raise both side to the 4th power
x=5/3

I think you messed up the sign....

Answer 2

particular this is an exponential carry out although the outcomes is mistaken. An fractional exponent signifies that some root may want to be calculated. therefore an exponent of one million/2 signifies that the sq. root of -4 may want to be determined. the oblong root of -4 is 2i (2 imaginary)