Questions: If f(x) = 5x + 3, g(x) = 3x^2, and h(x) = sqrt(x - 4), find the following: h(g(x)) =

Solution Steps

To find \( h(g(x)) \), we need to substitute the function \( g(x) \) into the function \( h(x) \). This means replacing the variable \( x \) in \( h(x) = \sqrt{x-4} \) with the expression for \( g(x) = 3x^2 \). The resulting expression will be \( h(g(x)) = \sqrt{3x^2 - 4} \).

We have the following functions:

• \( f(x) = 5x + 3 \)
• \( g(x) = 3x^2 \)
• \( h(x) = \sqrt{x - 4} \)

To find \( h(g(x)) \), we substitute \( g(x) \) into \( h(x) \): \[ h(g(x)) = h(3x^2) = \sqrt{3x^2 - 4} \]

Final Answer