Question

f(x)=x^{2}+9 and g(x)=x^{2}-8, find the
following functions. a. (f * g) (x); b. (g * f)(x) c. (f *
g)(4);

d. (g * f)(4)

Answer #1

Given that

f(x) = x^{2}+9 and

g(x) = x^{2}-8

a. (f * g)(x)= f(x) g(x)

= (x^{2}+9) (x^{2}-8)

= x^{2} x^{2} -
x^{2} 8 +9
x^{2} -98

= x^{4}- 8x^{2}+9x^{2} -72

= x^{4}+x^{2}-72

b. (g * f)(x)= g(x) f(x)

= (x^{2}-8) (x^{2}+9)

= x^{2} x^{2}
+x^{2} 9 -8
x^{2} -89

= x^{4}+ 9x^{2}-8x^{2}
-72

= x^{4}+x^{2}-72.

c. Since (f * g)(x)= x^{4}+x^{2}-72
................(1)

putting x=4 in above equation ,we get

(f * g)(4)= 4^{4}+4^{2}-72

= 256+16-72

=200

d. Since (g * f)(x)= x^{4}+x^{2}-72
................(2)

putting x=4 in above equation ,we get

(g * f)(4)= 4^{4}+4^{2}-72

= 256+16-72

=200

Find the derivative of the following functions
(a) f(x) = ln(√x3 −2x)
(b) g(x) =√x2 + 3 x3 −5x + 1
.

1. Let f(x)=x2−9 and g(x)=15−x.
Perform the composition or operation indicated.
(fg)(−8)=
2. Let f(x)=x2−8 and g(x)=16−x.
Perform the composition or operation indicated.
(f/g)(7)=
3. Let f(x)=5x+4 and g(x)e=4x−7. Find (f+g)(x),(f−g)(x),
(fg)(x), and (f/g)(x)
Give the domain of each.

For f(x) = x^2+6 and g(x) = x^2-5 find the following
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a.) (f o g)(x)
b.) (g o f) (x)
c.) (f o g) (4)
d.) (g o f) (4)

Given f′(x) = (9-x)2/ (x2+9)2
and f′′(x) = (2x(x2-27)/ (x2+ 9)3
, answer the following ques-
tions:
(a) Find the interval where f(x) is increasing and decreasing.
(b) At what values of x do the local maximum and local minimum
occur?
(c) Find the intervals of concavity.
(d) At what values of x do the inflection points occur?

1)If f(x)=2x-2 and g(x)=3x+9, find the following. a)
f(g(x))=? b) g(f(x))=? c) f(f(x))=?
2)Let f(x)=x^2 and g(x)=6x-16. Find the following: a)
f(3)+g(3)=? b) f(3)*g(3)=? c) f(g(3))=? d) g(f(3))=?
3) For g(x)=x^2+3x+4, find and simplify
g(3+h)-g(3)=?
Please break down in detail. Please and Thank
you

Find the derivatives of each of the following functions. DO NOT
simplify your answers.
(a) f(x) = 103x (3x5+ x − 1)4
(b) g(x) = ln(x3 + x) /
x2 − 4
(c) h(x) = tan-1(xex)
(d) k(x) = sin(x)cos(x)

Find each of the following functions. f(x) = 4 − 4x, g(x) =
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(a) f ∘ g and State the domain of the function. (Enter your
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(b) g ∘ f and State the domain of the function. (Enter your
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(c) f ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(d) g ∘ g and State the domain of the function. (Enter your
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Let f(x)=3x4+8 and g(x)=x+4. (f∘g)(x)=
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1. Differentiate the following functions. Do not simplify.
(a) f(x) = x^7 tan(x)
(b) g(x) = sin(x) / 5x + ex
(c) h(x) = (x^4 + 3x^2 - 6)^5
(d) i(x) = 4e^sin(9x)
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(g) L(x) = 4 csc^-1 (x2)
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