Answer:
Proved!
Step-by-step explanation:
For two functions f(x) and g(x) to be inverses of each other then;
f(g(x)) = x and g(f(x)) = x condition must be satisfied.
Checking: A. f(x) = 7x³ + 10 and g(x) = ∛[tex]\frac{x - 10}{7}[/tex]
So f(g(x)) = 7([tex]\sqrt[3]{(x- 10)/7}[/tex])³ + 10
We get; 7([tex]\frac{x - 10}{7}[/tex]) + 10 = x - 10 + 10 = x (*This is correct!)
So g(f(x)) = [tex]\sqrt[3]{((7x^3 + 10) - 10)/7}[/tex]
Ten cancels out and we are left with;
[tex]\sqrt[3]{7x^3/7}[/tex] = [tex]\sqrt[3]{x^3}[/tex] = x (* This is also correct!)
