Question: The function \( h \) is defined by \( h(x) = 3x^2 + 7 \). Find \( h(5x) \). \( h(5x) =…

The function \( h \) is defined by \( h(x) = 3x^2 + 7 \).

Find \( h(5x) \).

\( h(5x) = \boxed{\phantom{0}} \)

Solution

The function \( h \) is defined by \[ h(x) = 3x^2 + 7 \] To find \( h(5x) \), substitute \( 5x \) for \( x \) in the function. First, replace \( x \) with \( 5x \) in the equation: \[ h(5x) = 3(5x)^2 + 7 \] Next, calculate \( (5x)^2 \): \[ (5x)^2 = 25x^2 \] Now substitute back into the equation: \[ h(5x) = 3 \cdot 25x^2 + 7 \] Multiply: \[ h(5x) = 75x^2 + 7 \] Thus, \[ h(5x) = 75x^2 + 7 \]