Use the functions f(x)=−x2+4 and g(x)=4x+4 to answer parts​ (a)-(g).

Question

Use the functions

f(x)=−x2+4

and

g(x)=4x+4

to answer parts​ (a)-(g).

​(a) Solve	f(x)=0.	​(d) Solve	f(x)>0.	​(g) Solve	f(x)≥4.
​(b) Solve	g(x)=0.	​(e) Solve	g(x)≤0.
​(c) Solve	f(x)=g(x).	​(f) Solve	f(x)>g(x).

Question content area bottom

Part 1

​(a) The solution to

f(x)=0

is

x=negative 2 comma 2−2,2.

​(Type an integer or a fraction. Use a comma to separate answers as​ needed.)

Part 2

​(b) The solution to

g(x)=0

is

x=negative 1−1.

​(Type an integer or a fraction. Use a comma to separate answers as​ needed.)

Part 3

​(c) The solution of

f(x)=g(x)

is

x=negative 4 comma 0−4,0.

​(Type an integer or a fraction. Use a comma to separate answers as​ needed.)

Part 4

​(d) Solve

f(x)>0.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.

A.

The solution set is

enter your response here.

​(Type your answer in interval notation. Simplify your answer. Type an exact​ answer, using radicals as needed. Use integers or fractions for any numbers in the​ expression.)

B.

The solution set is the set of all real numbers.

C.

The solution set is the empty set.

Answer 1

If f(x)=0

0 = -x²+4

x²=4

x = -2,2

If g(x)=0

0=4x+4

-4=4x

x = -1

If f(x)=g(x)

-x²+4=4x+4

0 = x²+4x

0 = x(x+4)

x = -4,0

If f(x)>0

-x²+4>0

4>x²

2>|x|

|x|<2

-2<x<2

Hope this helped! Remember that √(x²) = |x| because the domain of √x is positive, so √(x²) also follows this rule.

Answer 2

-2x² + 4 > 0

x² - 2 < 0

(x - √2)(x + √2) < 0

x - √2 > 0 and x + √2 < 0

or

x - √2 < 0 and x + √2 > 0

Can you solve the two inequalities and answer?