Find f(x) if it is known that f(x+3)=4x+12
If f(x+3) = 4x + 12
the f((x-3)+3) = 4(x-3)+12
f(x) = 4x
To find f(x), we need to isolate x in the given equation.
Given: f(x+3) = 4x + 12
Step 1: Let's substitute y = x + 3 in the equation to simplify it further:
f(y) = 4(y - 3) + 12
Step 2: Distribute the 4 to each term inside the parentheses:
f(y) = 4y - 12 + 12
Step 3: Simplify the equation:
f(y) = 4y
Step 4: Replace y with (x + 3) to get the final expression for f(x):
f(x) = 4(x + 3)
Simplifying further:
f(x) = 4x + 12
Therefore, f(x) = 4x + 12.
To find f(x), you can start by replacing the x in the given equation f(x+3) = 4x + 12 with x-3. This will allow you to express f(x) in terms of x without the "+3":
f(x) = 4(x-3) + 12
Now simplify the equation:
f(x) = 4x - 12 + 12
The -12 and +12 cancel each other out, leaving you with:
f(x) = 4x
Therefore, the function f(x) is f(x) = 4x.