hello

basically if you have a function f(x) and you plug in -x and get the same function back, its an even function. if you get the opposite function back then its odd

for example f(x) = x^2 + 3f(-x) = (-x)^2 + 3 = x^2 + 3 = f(x) therefore its even

there's only one side

u can only divide both sides if there's another side

so the answer is

it's decomposing an expression into the product of smaller expressions

remember the rule (a^2-b^2) = (a+b)(a-b)

in this case your a^2 = 4x^2square root both sides and a = 2xdo the same with b^2 = 49b = 7plug in your a and b into (a+b)(a-b)

set the denominator equal to 0

x - 4 = 0x = 4

so all you have to do is plug in the g(x) function for wherever there's an x in the f(x) function

so since f(x) = x^2 - 8, and g(x) = sqrt(2x^2 - 2x), you replace the x in f(x) with sqrt(2x^2 - 2x)

f(g(x)) = (sqrt(2x^2 - 2x))^2 - 8f(g(x)) = 2x^2 - 2x - 8

that's your f(g(x)), and since you're solving for f(g(x)) = -5, just set that equation equal to -5

2x^2 - 2x - 8 = -52x^2 - 2x - 3 = 0

then when you use quadratic formula to solve for x, you get

x = (1 ± √7)/2

sin pi/6 = 1/2

Arcsin(x) with a capital letter is a restricted function

ok so f(x) = 2x + 5, and g(x) = x^2 + 1

so to find f(-2) + g(5) find each of those separately first

so f(-2) = 2*-2 + 5 = -4 + 5 = 1and g(5) = 5^2 + 1 = 26

and since ur finding f(-2) + g(5) just add them together

yeah just plug in 3 for x!

ok so basically the number line from -3 to 3 contains all the values from -3 to 3 right? so when they give you something like x < -2, they're asking you to shade all the values on the line that are less than two. since it's a <, that means it's not inclusive of -2, so you draw an open circle around -2 and then shade everything below -2, because everything below -2 is x < -2

with x ≥ 1, since it's a ≥ sign, that means it's inclusive of 1. so basically, it's asking what x values are all greater than and equal to 1 on the line. everything above 1, including 1, should be shaded then b/c that satisfies x ≥ 1

y = 3(2)^x

exponential growth equation is y = a(r)^x where a is the initial amount and r is the growth factor

so you plug in 3 for a, since there are 3 fish initially, and since it doubles every month, the r value is 2

Complementary angles are angles that add up to 90 degrees. Supplementary angles are angles that add up to 180 degrees. 

so to find the complement, you subtract from 90.

complement of (x+3) is (90-x-3) = (87-x)

supplement of (x+3) is (180-x-3) = (177-x)

complement of (2x-3) is (90 - 2x + 3) = (93-2x)