Let f left-parenthesis x right-parenthesis equals Start Root x End Root and lower g left parenthesis x right parenthesis equals 3 x plus 2. Find the range of left-parenthesis f dot g right-parenthesis left-parenthesis x right-parenthesis.

Question

(1 point)
Responses

left-bracket 0 comma infinity right-parenthesis
- image with description: left-bracket 0 comma infinity right-parenthesis - - no response given

left-bracket 2 comma infinity right-parenthesis
- image with description: left-bracket 2 comma infinity right-parenthesis - - no response given

left-parenthesis negative infinity comma 0 right-parenthesis union left-parenthesis 0 comma infinity right-parenthesis
- image with description: left-parenthesis negative infinity comma 0 right-parenthesis union left-parenthesis 0 comma infinity right-parenthesis - - no response given

left-parenthesis negative infinity comma negative Start Fraction two over 3 End Fraction right-parenthesis union left-parenthesis negative Start Fraction 2 over 3 End Fraction comma 0 right-parenthesis union left-parenthesis 0 comma infinity right-parenthesis

Answer 1

The range of f(g(x)) can be found by substituting g(x) into f(x) and determining the possible values of f(g(x)).

First, substitute g(x) = 3x + 2 into f(x):

f(g(x)) = f(3x + 2) = √(3x + 2)

To find the range, we need to determine the possible values of √(3x + 2).

Since the square root function is always non-negative, the range of √(3x + 2) is [0, infinity).

Therefore, the range of f(g(x)) is left-bracket 0, infinity)