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Consider the functions below. f(x) = \sqrt{x}, g(x) = \sqrt{x} (a) Find each of the following. fog= gof= Find the domain of fog. (Enter your answer using interval notation.) 

          Consider the functions below.
f(x) = \sqrt{x}, g(x) = \sqrt{x}
(a) Find each of the following.
fog=
gof=
Find the domain of fog. (Enter your answer using interval notation.)
Consider the functions below. f(x) = √(x), g(x) = √(x) (a) Find each of the following. fog= gof= Find the domain of fog. (Enter your answer using interval notation.)

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Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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Consider the functions below. f(x)=sqrt(x),g(x)=sqrt(x) (a) Find each of the following. f@g= g@f= Find the domain of f@g. (Enter your answer using interval notation.) Consider the functions below. f(x=xgx=x (a) Find each of the following fog= gof= Find the domain of f o g. (Enter your answer using interval notation.
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Transcript

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00:01 Given the following functions f and g, f plus g of x would be 5 over x plus 6 plus x plus 6, which is a common denominator.
00:11 So it's 5 plus x over x plus 6, the common denominator.
00:16 The domain in interval notation would be all reals except for negative 6 because if x is negative 6, we're divided by 0.
00:23 So we say from negative infinity to negative 6 not included, union or comma, negative 6 to infinity.
00:33 F minus g of x would be 5 over x plus 6 minus x over x plus 6 so subtract fractions we get a common denominator so it's the numerator 5 minus x over x plus 6 the domain same negative infinity negative 6 not included you need negative 6 not included to infinity f times g of x would be 5 over x plus 6 times negative x over x plus 6 times negative x over x plus 6 you multiply fraction straight across with negative 5x over x squared plus 12x plus 36 still x cannot be negative 6 so negative infinity to negative 6 not included you need negative 6 not included to infinity and then when we divide 5 over x plus 6 when you divide you really multiply by the reciprocal and so we're multiplying by x plus 6 and so we're multiplying by x plus 6 over negative x.
01:38 So the x plus sixes will cancel and we have negative 5 over x...
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