Final answer:
To find f²(x) given f(x) = 5 cos(7 ln(x)), square each term in the function and simplify the equation to get f²(x) = 25 cos²(7 ln(x)).
Step-by-step explanation:
To find f²(x) given f(x) = 5 cos(7 ln(x)), we need to square the function. Square each term in the function:
f²(x) = (5 cos(7 ln(x)))²
Apply the square to both the coefficient (5) and the function (cos(7 ln(x)):
f²(x) = 5² * (cos(7 ln(x)))²
Simplify the equation:
f²(x) = 25 * cos²(7 ln(x))
Therefore, f²(x) = 25 cos²(7 ln(x)).