Answer:
Explanation:
To find the value of f(X+1) - f(X) when f(X) = 4^x, we need to substitute X+1 and X into the function and then subtract the two values.
Given:
f(X) = 4^x
Step 1: Substitute X+1 into the function
f(X+1) = 4^(X+1)
Step 2: Substitute X into the function
f(X) = 4^X
Step 3: Subtract the two values
f(X+1) - f(X) = 4^(X+1) - 4^X
To simplify this expression, we can use the properties of exponents. The key property here is that when you subtract two numbers with the same base (in this case, 4), you can divide the exponents.
Step 4: Simplify using the exponent property
f(X+1) - f(X) = 4^(X+1) - 4^X
= 4 * 4^X - 4^X
= 4^X * (4 - 1)
= 3 * 4^X
Therefore, f(X+1) - f(X) simplifies to 3 * 4^X.
In conclusion, if f(X) = 4^x, then f(X+1) - f(X) is equal to 3 times 4 raised to the power of X.
I hope this explanation helps! If you have any further questions, feel free to ask.