Question

Given f(x) = 2x^{2} + 1 and g(x) = 6x − 9,

find the following.

(a) f(g(2))

(b) f(g(x))

(c) g(f(x))

(d) (g ∘ g)(x)

(e) (f ∘ f)(−2)

Answer #1

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

Given the functions: f(x) = 6x+9 and g(x) =7x-4, determine each of
the following. Give your answers as simplified expressions written
in descending order.
(F+g)(x)=
(F-g)(x)=
(F•g)(x)=
(F/g)(x)=

3. Given f(x) = arctan x and g(x) = e^x , find the
following:
a. (f + g)(1)
b. (fg)(0)
c. (f ◦ g)(0)
d. (g ◦ f)(0)

1. Consider the function.
f(x) = 6x − 9
(a) Find the inverse function of f.
(b) Graph f and f −1 on the same
set of coordinate axes.
(c) Describe the relationship between the graphs. The graphs of
f and f −1 are reflections of each
other across the line y =
(d) State the domain and range of f and f
−1. (Enter your answers using interval notation.)
2.
Consider the function.
f(x) = x+3/x
(a) Find the...

Find the inverse of the following:
A) f(x)= 6x+54.
B)g(x)= 3sqrt x+7

Given that f(x)=x^2-9 and g(x)=3x+16, find (g-f)(9), if it
exists.

f(x)=x2+9 and g(x)=x2-8, find the
following functions. a. (f * g) (x); b. (g * f)(x) c. (f *
g)(4);
d. (g * f)(4)

Given f''(x)=−36sin(6x) and f'(0)=1 and f(0)=−2 . Find f(π/6)
=

Find the derivative of the function.
(a) f(x) = ln (x) + 6x^(2) – 5
(b) f(x) = ln (x + 1)
(c) f(x) = 5 ln x
(d) f(x) = ln(x^(3) – 5x^(2) – 2x + 5)
(e) 2lnx / x
(f) x^(2) ln x

Find f(x).
1. f''(x) = (1/3) x^3 −3x^2 + 6x
2. f''(x) = −1 + 6x−12x^2, f(0) = 4, f'(0) = 12
3. f'''(x) = sinx, f(0) = 1, f'(0) = 2, f''(0) = 3

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