Question

Suppose that f(2) = −4, g(2) = 2, f '(2) = −5, and g'(2) = 1.

Find h'(2).

a. h(x)=2f(x)-5g(x)

h'(2)=?

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

h'(2)=?

c. h(x)=f(x)/g(x)

h'(2)=?

d. h(x)=g(x)/1+f(x)

h'(2)=?

Answer #1

Suppose that f(2) = −3, g(2) = 4, f '(2) = −1, and g'(2) = 5.
Find h'(2). (a) h(x) = 3f(x) − 5g(x) h'(2) h(x) = f(x)g(x) h'(2) =
h(x) = f(x) g(x) h'(2) =(d) h(x) = g(x) 1 + f(x) h'(2) =

Suppose the derivative of f exists, and assume that f(1) = 4,
and f'(1) = 5. Let g(x) = x^2f(x), and h(x) = f(x)/x-2
a) g' (1) = ??
find the equation of the tangent line to g(x) at x = 1
y = ??
b) h'(1) = ??
Find the equation of the tangent line to h(x) at x = 1
y = ??

Suppose f(1) = −1, f(2) = 0, g(1) = 2, g(2) = 7, and f 0 (1) =
1, f0 (2) = 4, g0 (1) = 8, g0 (2) = −4.
(a) Suppose h(x) = f(x^2 g(x)). Find h 0 (1).
(b) Suppose j(x) = f(x) sin(x − 1). Find j 0 (1).
(c) Suppose m(x) = ln(x)+arctan(x) e x+g(2x) . Find m0 (1).

Given F(2) = 1, F'(2) = 7, F(4) = 3, F′(4) = 7
and G (4) = 2 , G′(4)= 6, G(3)= 4, G′(3)=11,
find the following.
(a) H(4) if H(x) = F(G(x))
H(4) =
(b) H′(4) if H(x) = F(G(x))
H′(4) =
(c) H(4) if H(x) = G(F(x))
H(4) =
(d) H′(4) if H(x) = G(F(x))
H'(4)=

If f(2) = 3, f'(2) = 5, g(2) = 1, and g'(2) = 4, find h'(x) and
r'(x) if h(x) = 2(f(x))3/2 and r(x) = g(x) + p g(x), and determine
the greater value between h'(2) and r'(2).

Prob 5:
i) Suppose f: R → Z where ?(?) =[2? - 1]
a. If A = {x | 1 =< x =< 4}, find f(A).
b. If C = {-9, -8}, find f−1(C).
c. If D = {0.4, 0.5, 0.6}, find f−1(D).
(ii) Suppose g: A → B and f: B → C where A = {a, b, c, d}, B = {1,
2, 3}, C = {2, 3, 6, 8}, and g and f
are defined as g...

suppose and are functions that are differentiable at x=0 and
that f(1)=2, f'(1)=-1, g(1)=-2, and g'(1)=3. Find the value of
h'(1).
1) h(x)=f(x) g(x)
2) h(x)=xf(x) / x+g(x)

If f (2) = 1, \ f '(2) = - 3 and g (x) = log_2 (x ^ 2f (x) / cos (f (x)) then g' (2) is equal to:
a)-9.625983
B)-3.327777
c)-4.800967
d)-12.01444
E)The answer doesn´t exist

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

f(x) = (5)/(sqrt(4-x)), g(x)=x+4
1. find domain of f
2. domain of g
3. (f∘g)(x)
4. domain (f∘g)

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