Answer:
f(x) and g(x) are inverse functions
Step-by-step explanation:
In the two functions f(x) and g(x) if, f(g(x)) = g(f(x)) = x, then
f(x) and g(x) are inverse functions
Let us use this rule to solve the question
∵ f(x) = 3x²
∵ g(x) = 
→ Find f(g(x)) by substitute x in f(x) by g(x)
∴ f(g(x)) = 3()²
→ Cancel the square root with power 2
∴ f(g(x)) = 3(
)
→ Cancel the 3 up with the 3 down
∴ f(g(x)) = x
→ Find g(f(x)) by substitute x in g(x) by f(x)
∴ g(f(x)) = 
→ Cancel the 3 up with the 3 down
∴ g(f(x)) = 
→ Cancel the square root with power 2
∴ g(f(x)) = x
∵ f(g(x)) = g(f(x)) = x
→ By using the rule above
∴ f(x) and g(x) are inverse functions
Answer:
Step-by-step explanation:
The function is given.
To find : 
The input for the function f(x) is (a + 1).
Replace x with (a + 1).
Expand brackets.
Simplifying.
Answer:
(x-8)(x+3)
Step-by-step explanation:
1) Find out what are the factors of the constant?
2) Which of those add to equal the coefficient before the x value?
In this particular equation, we have the constant being 24. The first two factors that come to mind are 6 and 4, and 8 and 3. Since it is -24, we need one of these numbers to be negative.
Let's look at our "b" value, or the coefficient behind the x value, 5. Looking at our factors and thinking of addition (since one of them must be negative, it will most likely be subtraction instead of addition) I can see that
8+ −3=5
which is one of the factors of -24.
This means that we can factor our equation using these numbers, getting us the following:
(x−3)(x+8)
Hope this helped!
Answer:
37 is prime number
Step-by-step explanation:
To prove whether a number is a prime number, first try dividing it by 2, and see if you get a whole number. If you do, it can't be a prime number. If you don't get a whole number, next try dividing it by prime numbers: 3, 5, 7, 11 (9 is divisible by 3) and so on, always dividing by a prime number
