Suppose that f(x)= square root of x and g(x)= 3x-4 and you are asked to evaluvate the composite function f(g(0)).

What is the complication that occurs in trying to find that composite function value?

For waht values of x is it possible to evauvate f(g(x))?

Please help me with this question!

You can not take the square root of a negative number and get a real answer.

x>/= 4/3

The complication that occurs in trying to evaluate the composite function f(g(0)) is that g(0) is not defined. This is because g(x) involves multiplying x by 3 and subtracting 4, so when x = 0, the expression becomes 3(0) - 4, which results in -4. However, the function f(x) = √x is not defined for negative values of x, including -4. Therefore, we cannot evaluate f(g(0)) because one of the intermediate values in the composite function is not in the domain of f(x).

To determine for what values of x it is possible to evaluate f(g(x)), we need to consider the domain restrictions of the individual functions. The function f(x) = √x is defined for all non-negative real numbers, meaning x ≥ 0. The function g(x) = 3x - 4 is defined for all real numbers since there are no domain restrictions.

So, to evaluate f(g(x)), we need to find values of x such that g(x) is non-negative. In other words, we need to solve the inequality g(x) ≥ 0.

Substituting g(x) = 3x - 4 into the inequality, we have:

3x - 4 ≥ 0

Solving this inequality, we get:

3x ≥ 4
x ≥ 4/3

Therefore, for values of x greater than or equal to 4/3, it is possible to evaluate the composite function f(g(x)).