Let f be a function with f(x) > 0 for all x. Let g = 1/f. (1) If f is increasing in an interval around x0, what about g?
a) g is constant in an interval around x0.
b)We cannot tell whether g is increasing or decreasing in an interval around x0.
c)g is increasing in an interval around x0
d)g is decreasing in an interval around x0. e) g is zero in an interval around x0.
(2)If f has a local maximum at x1, what about g?
a)g has an inflection point at x1.
b) g has a local maximum at x1.
c) g has a local minimum at x1.
d) We cannot tell whether g has a local minimum or a local maximum at x1.e) g has both a local minimum and a local maximum at x1.
(3)If f is concave down at x2, what about g?
a) g is flat at x2.
b)g is increasing at x2.
c)g is concave down at x2.
d)g is concave up at x2.
e) We cannot tell whether g is concave up or concave down at x2.

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.