How Do You Find f(x) When the Value for x Contains Other Variables?

f(x) is function notation and tells you the variable the function is using
To evaluate a function in function notation, plug whatever is inside the parentheses in for the variable
Here our variable is 'x', so we need to plug in '5t+3' wherever we see an 'x'

1. f(x) is function notation and tells you the variable the function is using
2. To evaluate a function in function notation, plug whatever is inside the parentheses in for the variable
3. So if we had f(4) we would just replace all the x's with 4's in the function
1. When you have an expression like 5t+3 instead of a number, it's no different
2. Just replace each 'x' with '5t+3'
1. We need to plug in our expression, 5t+3, every time we have an x in the function
1. 'x' is the variable in the function
2. 5t+3 is what we're plugging in for x
1. f(x) is function notation
2. That means we're taking what's inside the parentheses and plugging it in in place of the variable
3. Though it might look like f•x, since we're using parentheses, that is NOT what it means
1. Now that we've plugging in our expression, we just need to simplify to get our final answer
1. We need to get rid of exponents first, so expand out the first term by multiplying 5t+3 by 5t+3
2. We can multiply 5t+3 times 5t+3 using FOIL
3. And we can also distribute the 4 into 5t+3
4. Like terms are terms with the same variables raised to the same power
5. So 15t, 15t, and 20t are like terms
6. And 9, 12, and 6 are like terms as well

Find f(5t + 3) for the function f(x) = x2 + 4x + 6