Question

What is the solution of the equation f(x) = g(x) ?

Answer 1

We are given the two functions $f(x) = x^{-\frac{1}{2} }$ and $g(x) = \sqrt{x} - \frac{3}{2}$. Since the question is asking us for the value of x when f(x) is equal to g(x), all we need to do is equate the respective expressions together. This is what the result should be:
$x^{-\frac{1}{2}} = \sqrt{x} - \frac{3}{2}$
Now, just solve for x. If you want to save some time, you can use logic and then algebra. To do this, look at the square root. We cannot have an imaginary number, so we can rule out the first two options. Now, we are left with x = 2 and x = 4. When we plug in each x-value to the equation, only 4 works out with a result of 0.5 = 0.5. Therefore, the solution to f(x) = g(x) is D) x = 4. Hope this helps and have a great day!