SOLUTION: For f(x)=(3x^2)+5and g(x)=7x-2, a. Verify: g(x + 2) &#8800; g(x) + g(2). b. Find (f � g)(x). c. Using the resulting function in (b), show that (f � g)(2) = f(2) � g(2)

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Question 960391: For f(x)=(3x^2)+5and g(x)=7x-2,
a. Verify: g(x + 2) ≠ g(x) + g(2).

b. Find (f � g)(x).

c. Using the resulting function in (b), show that (f � g)(2) = f(2) � g(2).
(The work should be different for each side of the equation.)

d. Is (fg)(0) =(f/g)(0)? Explain.

e. Find (f(x+h)-f(x))/h , h ≠ 0.
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!
For

a. Verify:

first find

and

substitute it in

b. Find
since
, we have

c. Using the resulting function in (b), show that .
(The work should be different for each side of the equation.)

d. Is ? Explain.

.....so, the product (on the left side of equation) could not be same as the quotient (on the right side of equation)

e. Find , .

SOLUTION: For f(x)=(3x^2)+5and g(x)=7x-2, a. Verify: g(x + 2) &#8800; g(x) + g(2). b. Find (f � g)(x). c. Using the resulting function in (b), show that (f � g)(2) = f(2) � g(2)

SOLUTION: For f(x)=(3x^2)+5and g(x)=7x-2, a. Verify: g(x + 2) ≠ g(x) + g(2). b. Find (f � g)(x). c. Using the resulting function in (b), show that (f � g)(2) = f(2) � g(2)