Question

the function h is defined by $h(x) = 3x^2 - 2$. find $h(4z)$. $h(4z) = $

Explanation:

Step1: Substitute \( x = 4z \) into \( h(x) \)

Given \( h(x) = 3x^2 - 2 \), replace \( x \) with \( 4z \). So we get \( h(4z) = 3(4z)^2 - 2 \).

Step2: Simplify \( (4z)^2 \)

Using the exponent rule \( (ab)^n = a^n b^n \), \( (4z)^2 = 4^2 \cdot z^2 = 16z^2 \). Then substitute back: \( h(4z) = 3 \cdot 16z^2 - 2 \).

Step3: Multiply 3 and 16

Calculate \( 3 \times 16 = 48 \), so \( h(4z) = 48z^2 - 2 \).

Answer:

\( 48z^2 - 2 \)