Let f(x)=9x-2 and g(x)=-x+3. find f(g(x)).
2 answers:
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Given
we have
Squaring both sides, we have
And finally
Note that, when we square both sides, we have to assume that
because we're assuming that this fraction equals a square root, which is positive.
So, if that fraction is positive you'll actually have roots: choose
and you'll have
Which is a valid solution. If, instead, the fraction is negative, you'll have extraneous roots: choose
and you'll have
Squaring both sides (and here's the mistake!!) you'd have
which is not a solution for the equation, if we plug it in we have
Which is clearly false
