1-8-3 composition of functions
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Find F of G of X&G of F of X and determine whether the pair
function F&G are inverses of each other.
So to find F of G of X, we're going to put the G equation X +
7 / 6 into the F equation every time we see the unknown.
So we're going to have 7 * X + 7 / 6 - 6.
So if we multiply this out, we get seven six X + 49 six -6.
We could think of that.
Six is over one.
So now we'd want to get a common denominator 7X over 6 + 49 / 6.
Six is really 36 / 6.
So seven X + 49 - 36 / 6 is going to give us seven X + 13 /
6.
Now to do G of F of X, we're going to take the G equation.
And every time we see the unknown, we're going to put in
the F equation.
So seven X - 6 + 7 all over six, we get seven X + 1 / 6.
Then we want to determine if they're inverses of each other.
They're not inverses of each other.
If they had been inverses of each other when we did our
manipulation, F of G of X&G of F of X would have given out
X.