To me personally, the first bit f(g(x)) is easy and the domain is tricky. Let's try explain this.
A function takes an input number and returns an output number depending on the function. Look at f(x) = x+3, if we let the input number be 2 then we say that f(2) = 5. We could do f(π) to give us π+3 or even f(x²) to give us x² +3. The trick is to substitute the input into the function equation.
You have been asked to find f(g(x)). You know f(x) =
. Putting numbers in at this point would be easy (try work out f(2), you'll do it really quick) but you have to put in g(x).
f(g(x)) =
we also know that g(x) =
so we can say that
f(g(x)) =
and that is f(g(x)) but the question requires that we simplify it so
f(g(x)) =
Now for the tricky bit (for me, at least). The domain is the full set of values that you can 'put in to' the function and still get a real value out. So how do we work out what numbers 'break' the function? I like to use the fact that DIVIDING BY ZERO IS IMPOSSIBLE. What value of x can we put into the function to make it so the function is being divided by 0? i.e. 1-2x = 0 solve that and you have a value of x that isn't part of the domain.
This means the domain is all real numbers EXCEPT the solution to that equation. (Because if we put that value into f(g(x)) it's impossible to get a value out.)
[I know this was a lot to read, if you have any questions or don't get anything feel free to message me or leave a comment.]
If it took you (one person) 3 days to build a doghouse, then it should take 2 people to build it in half the time. So all we have to do is split 3 days in 2.
3/2 = 1.5
So it would take 1 1/2 days or 36 hours for 2 people to complete the doghouse.
Remark
Supplementary angles add up to 180o.
Givens
<1 = 124
<2 = 2x + 4
I imagine you are looking for either x or <2.
Equation
<1 + <2 = 180 Substitute the givens
124 + 2x + 4 = 180 Collect like terms on the left.
128 + 2x = 180 Subtract 128 from both sides
2x = 180 - 128 Collect like terms on the right
2x = 52 divide by 2
x = 52/2
x = 26 <<<<<<<<< answer
<1 = 124
<2 = 2x + 4 = 2*26 + 4
<2 = 52 + 4
<2 = 56 <<<<<<<< answer
We need choices if you want an exact answer.
1) Expression 1: 16x^3 y
2) Expression 2: 24 xy^5
Procedure:
1) find the greatest common factor of the coefficients, 16 and 24:
16 = 2^4
24 = (2^3)*3
=> greatest common factor = 2^3 = 8
2) find the greatest common factor of x^3 y and xy^5
That is the common letters each raised to the lowest power:
=> xy
3) Then, the result is 8xy
The length of the picture would be 10 inches. If the frame needs to be 34, that means 7+7 for the width and 10+10 for the length.