Final Answer:
h(5x) = 75x^2 - 7, is obtained by substituting (5x) into the original function h(x) = 3x^2 - 7, following the rules of function transformation and simplification. This yields the expression (75x^2 - 7) as the transformed function.
Step-by-step explanation:
The given function ( h(x) = 3x^2 - 7 ) is transformed into ( h(5x) ) by replacing ( x ) with ( 5x). This results in the expression ( 3(5x)^2 - 7 ).
To simplify, first square the ( 5x ), yielding (3 times 25x^2 - 7 ). Further simplification gives ( 75x^2 - 7 ), which is the final answer.
In essence, the original function ( h(x) ) represents the process of squaring ( x ), multiplying by 3, and subtracting 7. When applied to ( 5x ), this process is still followed, resulting in ( 75x^2 - 7 ).
This means that for any given value of ( x ), the function ( h(5x) ) will output ( 75x^2 - 7 ).