Question

Select the true statement.

A.
Neither function is even.
B.
Both functions are even.
C.
Only function g is even.
D.
Only function f is even.

Answer 1

Answer:

only G is even

it's obvious that g is even. g(x)= |x|

for $f$ ...

it's a quadratic equation with roots -1 and 4,

thus the equation will be

$y= k(x^2 -(-1+4)x+(-1) \times 4)$

(if you have roots of a quadratic equation, the equation is

$k(x^2-(\text{sum of roots}x+\text{product of roots}$

or

$y=k(x^2-3x-4)$

now, put the point (0,4)

$4=k×-4 \implies k= -1$

so the equation is

$y=-x^2-3x+4$

now if you put

$x \rightarrow -x$

you get

$x^2+3x+4$

which is not the same.

hence

$f(x) \ne f(-x)$